Solve for X:
\qquad
A = expr(["+", ["*", B, X], ["*", C, ["+",
["*", D, X], E]]])
X =
SOLUTION
Try simplifying the right side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{C}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{C}:
\qquad\begin{eqnarray}
A &=& expr(["*", B, X]) +
\pink{C}\blue{(expr(["+", ["*", D, X], E]))} \\ \\
A &=& expr(["*", B, X]) +
\pink{(C)}\blue{(expr(["*", D, X]))} +
\pink{(C)}\blue{(E)}
\end{eqnarray}
Multiply:
\qquad
A =
expr(["+", ["*", B, X], ["*", C * D, X], C * E])
Combine the
X terms:
\qquad\begin{eqnarray}
A &=&
\blue{expr(["+", ["*", B, X], ["*", C * D, X]])} + C * E \\ \\
A &=&
\blue{expr(["*", B + C * D, X])} + C * E
\end{eqnarray}
Add
\green{abs(C * E)}
to both sides
to isolate the X term on the
right side:
Subtract
\green{abs(C * E)}
from both sides
to isolate the X term on the
right side:
\qquad\begin{eqnarray}
A &=&
expr(["*", B + C * D, X]) \green{{} + C * E} \\ \\
\green{{}+-C * E} &&
\green{{}+-C * E} \\ \\
A - C * E &=&
expr(["*", B + C * D, X])
\end{eqnarray}
Divide both sides by
\green{B + C * D}
to isolate X:
\qquad\begin{eqnarray}
A - C * E &=&
expr(["*", B + C * D, X]) \\ \\
\dfrac{A - C * E}
{\green{B + C * D}} &=&
\dfrac{\green{\cancel{B + C * D}}
X}{\green{\cancel{B + C * D}}}
\end{eqnarray}
Simplify:
\qquad
fractionReduce(A - C * E, B + C * D)
= X
Solve for X:
\qquad
A = expr(["+", ["*", B, ["+", C, ["*", D, X]]],
["*", E, X]])
X =
SOLUTION
Try simplifying the right side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{B}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{B}:
\qquad\begin{eqnarray}
A &=&
\pink{B}\blue{(expr(["+", C, ["*", D, X]]))} +
expr(["*", E, X]) \\ \\
A &=&
\pink{(B)}\blue{(C)} +
\pink{(B)}\blue{(expr(["*", D, X]))} +
expr(["*", E, X])
\end{eqnarray}
Multiply:
\qquad
A =
expr(["+", B * C, ["*", B * D, X], ["*", E, X]])
Combine the
X terms:
\qquad\begin{eqnarray}
A &=&
B * C \blue{{} + expr(["*", B * D, X])}
\blue{{} + expr(["*", E, X])} \\ \\
A &=&
B * C \blue{{} + expr(["*", B * D + E, X])}
\end{eqnarray}
Add
\green{abs(B * C)}
to both sides
to isolate the X term on the
right side:
Subtract
\green{abs(B * C)}
from both sides
to isolate the X term on the
right side:
\qquad\begin{eqnarray}
A &=&
\green{B * C} + expr(["*", B * D + E, X]) \\ \\
\green{{}+-B * C} &&
\green{{}+-B * C} \\ \\
A - B * C &=&
expr(["*", B * D + E, X])
\end{eqnarray}
Divide both sides by
\green{B * D + E}
to isolate X:
\qquad\begin{eqnarray}
A - B * C &=&
expr(["*", B * D + E, X]) \\ \\
\dfrac{A - B * C}
{\green{B * D + E}} &=&
\dfrac{\green{\cancel{B * D + E}}
X}{\green{\cancel{B * D + E}}}
\end{eqnarray}
Simplify:
\qquad
fractionReduce(A - B * C, B * D + E)
= X
Solve for X:
\qquad
expr(["*", A, ["+", ["*", B, X], C]]) =
expr(["+", ["*", D, ["+", E, ["*", F, X]]],
["*", G, X]])
X =
SOLUTION
Try simplifying each side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{A}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{A}:
\qquad\begin{eqnarray}
\pink{A}\blue{(expr(["+", ["*", B, X], C]))} &=&
expr(["+", ["*", D, ["+", E, ["*", F, X]]], ["*", G, X]]) \\ \\
\pink{(A)}\blue{(expr(["*", B, X]))} +
\pink{(A)}\blue{(C)} &=&
expr(["+", ["*", D, ["+", E, ["*", F, X]]], ["*", G, X]])
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A * B, X], A * C]) =
expr(["+", ["*", D, ["+", E, ["*", F, X]]], ["*", G, X]])
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{D}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{D}:
\qquad\begin{eqnarray}
expr(["+", ["*", A * B, X], A * C]) &=&
\pink{(D)}\blue{(expr(["+", E, ["*", F, X]]))} +
expr(["*", G, X]) \\ \\
expr(["+", ["*", A * B, X], A * C]) &=&
\pink{(D)} \blue{(E)} +
\pink{(D)}
\blue{(expr(["*", F, X]))} +
expr(["*", G, X])
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A * B, X], A * C]) =
expr(["+", D * E, ["*", D * F, X], ["*", G, X]])
Combine the
X terms:
\qquad\begin{eqnarray}
expr(["+", ["*", A * B, X], A * C]) &=&
D * E \blue{{} + expr(["+", ["*", D * F, X], ["*", G, X]])} \\ \\
expr(["+", ["*", A * B, X], A * C]) &=&
D * E \blue{{} + expr(["*", D * F + G, X])}
\end{eqnarray}
Add
\green{expr(["*", abs(D * F + G), X])}
to both
sides to eliminate the X term
from the right side:
Subtract
\green{expr(["*", abs(D * F + G), X])}
from both
sides to eliminate the X term
from the right side:
\qquad\begin{eqnarray}
expr(["+", ["*", A * B, X], A * C]) &=&
D * E \green{{} + expr(["*", D * F + G, X])} \\ \\
\green{{}+expr(["*", -(D * F + G), X])}
&& \green{{} +
expr(["*", -(D * F + G), X])} \\ \\
expr(["+", ["*", A * B, X], A * C])
\green{+expr(["*", -(D * F + G), X])} &=&
D * E
\end{eqnarray}
Combine the
X terms:
\qquad\begin{eqnarray}
\blue{expr(["*", A * B, X])} + A * C
\blue{+expr(["*", -(D * F + G), X])} &=&
D * E \\ \\
\blue{expr(["*", (A * B) - (D * F + G), X])} + A * C &=&
D * E
\end{eqnarray}
Add
\green{abs(A * C)}
to both sides
to isolate the X term on the
left side:
Subtract
\green{abs(A * C)}
from both sides
to isolate the X term on the
left side:
\qquad\begin{eqnarray}
expr(["*", (A * B) - (D * F + G), X]) \green{{} + A * C} &=&
D * E \\ \\
\green{{}+-A * C} &&
\green{{}+-A * C} \\ \\
expr(["*", (A * B) - (D * F + G), X])
&=& D * E - A * C
\end{eqnarray}
Divide both sides by
\green{(A * B) - (D * F + G)}
to isolate X:
\qquad\begin{eqnarray}
expr(["*", (A * B) - (D * F + G), X])
&=& D * E - A * C \\ \\
\dfrac{\green{\cancel{(A * B) - (D * F + G)}}
X}{\green{\cancel{(A * B) - (D * F + G)}}}
&=& \dfrac{D * E - A * C}
{\green{(A * B) - (D * F + G)}} \\ \\
\end{eqnarray}
Simplify:
\qquad
X
= fractionReduce(D * E - A * C, (A * B) - (D * F + G))
Solve for X:
\qquad
expr(["+", ["*", A, X], ["*", B, ["+",
["*", C, X], D]]]) =
expr(["+", ["*", E, X], F])
X =
SOLUTION
Try simplifying the left side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{B}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{B}:
\qquad\begin{eqnarray}
expr(["*", A, X]) +
\pink{B}
\blue{(expr(["+", ["*", C, X], D]))}
&=&
expr(["+", ["*", E, X], F]) \\ \\
expr(["*", A, X]) +
\pink{(B)}
\blue{(expr(["*", C, X]))} +
\pink{(B)}
\blue{(D)} &=&
expr(["+", ["*", E, X], F])
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A, X], ["*", B * C, X],
B * D]) = expr(["+", ["*", E, X],
F])
Add
\green{expr(["*", abs(E), X])}
to both
sides to eliminate the X term
from the right side:
Subtract
\green{expr(["*", abs(E), X])}
from both
sides to eliminate the X term
from the right side:
\qquad\begin{eqnarray}
expr(["+", ["*", A, X], ["*", B * C, X],
B * D]) &=&
\green{expr(["*", E, X])} +
F \\ \\
\green{{}+expr(["*", -E, X])}
&=& \green{{} +
expr(["*", -E, X])} \\ \\
expr(["+", ["*", A, X], ["*", B * C, X],
B * D]) \green{
+expr(["*", -E, X])} &=&
F
\end{eqnarray}
Combine the
X terms:
\qquad\begin{eqnarray}
\blue{expr(["+", ["*", A, X],
["*", B * C, X]])} + B * D
\blue{+expr(["*", -E, X])} &=&
F \\ \\
\blue{expr(["*", A + B * C - E, X])} +
B * D & = & F
\end{eqnarray}
Add
\green{abs(B * D)}
to both sides
to isolate the X term on the
left side:
Subtract
\green{abs(B * D)}
from both sides
to isolate the X term on the
left side:
\qquad\begin{eqnarray}
expr(["*", A + B * C - E, X])
\green{+ B * D} & = &
F \\ \\
\green{{}+-B * D} &&
\green{{}+-B * D} \\ \\
expr(["*", A + B * C - E, X])
&=& F - B * D
\end{eqnarray}
Divide both sides by
\green{A + B * C - E}
to isolate X:
\qquad\begin{eqnarray}
\green{A + B * C - E}X &=&
F - B * D \\ \\
\dfrac{\green{\cancel{A + B * C - E}}
X}{\green{\cancel{A + B * C - E}}}
&=& \dfrac{F - B * D}
{\green{A + B * C - E}} \\ \\
\end{eqnarray}
Simplify:
\qquad
X
= fractionReduce(F - B * D, A + B * C - E)
Solve for X:
\qquad
expr(["+", A, ["*", B, X]]) =
expr(["*", C, ["+", ["*", D, X], E]])
X =
SOLUTION
Try simplifying the right side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{C}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{C}:
\qquad\begin{eqnarray}
expr(["+", A, ["*", B, X]]) &=&
\pink{C}\blue{(expr(["+", ["*", D, X], E]))} \\ \\
expr(["+", A, ["*", B, X]]) &=&
\pink{(C)}\blue{(expr(["*", D, X]))} +
\pink{(C)}\blue{(E)}
\end{eqnarray}
Multiply:
\qquad
expr(["+", A, ["*", B, X]]) =
expr(["+", ["*", C * D, X], C * E])
Add
\green{expr(["*", abs(C * D), X])}
to both
sides to eliminate the X term
from the right side:
Subtract
\green{expr(["*", abs(C * D), X])}
from both
sides to eliminate the X term
from the right side:
\qquad\begin{eqnarray}
expr(["+", A, ["*", B, X]]) &=&
\green{expr(["*", C * D, X])} + C * E \\ \\
\green{{}+expr(["*", -C * D, X])}
&& \green{{} +
expr(["*", -C * D, X])} \\ \\
expr(["+", A, ["*", B, X]])
\green{{} + expr(["*", -C * D, X])} &=&
C * E
\end{eqnarray}
Combine the
X terms:
\qquad\begin{eqnarray}
A \blue{{} + expr(["+", ["*", B, X], ["*", -C * D, X]])}
&=& C * E \\ \\
A \blue{{} + expr(["*", B - C * D, X])} &=& C * E
\end{eqnarray}
Add
\green{abs(A)}
to both sides
to isolate the X term on the
left side:
Subtract
\green{abs(A)}
from both sides
to isolate the X term on the
left side:
\qquad\begin{eqnarray}
\green{A} + expr(["*", B - C * D, X]) &=& C * E \\ \\
\green{{}+-A} &&
\green{{}+-A} \\ \\
expr(["*", B - C * D, X]) &=& C * E - A
\end{eqnarray}
Divide both sides by
\green{B - C * D}
to isolate X:
\qquad\begin{eqnarray}
\green{B - C * D}X &=&
C * E - A \\ \\
\dfrac{\green{\cancel{B - C * D}}
X}{\green{\cancel{B - C * D}}}
&=& \dfrac{C * E - A}
{\green{B - C * D}} \\ \\
\end{eqnarray}
Simplify:
\qquad
X = fractionReduce(C * E - A, B - C * D)
Solve for X:
\qquad
expr(["+", ["*", A, X], ["*", B, ["+", C, ["*", D, X]]]]) = E
X =
SOLUTION
Try simplifying the left side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{B}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{B}:
\qquad\begin{eqnarray}
expr(["*", A, X]) +
\pink{B}\blue{(expr(["+", C, ["*", D, X]]))} &=&
E \\ \\
expr(["*", A, X]) +
\pink{(B)}\blue{(C)} +
\pink{(B)}\blue{(expr(["*", D, X]))} &=&
E
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A, X], B * C, ["*", B * D, X]]) =
E
Combine the
X terms:
\qquad\begin{eqnarray}
\blue{expr(["*", A, X])} + B * C \blue{{}+ expr(["*", B * D, X])} &=& E \\ \\
\blue{expr(["*", A + B * D, X])} + B * C &=& E
\end{eqnarray}
Add
\green{abs(B * C)}
to both sides
to isolate the X term on the
left side:
Subtract
\green{abs(B * C)}
from both sides
to isolate the X term on the
left side:
\qquad\begin{eqnarray}
expr(["*", A + B * D, X]) \green{{} + B * C} &=& E \\ \\
\green{{}+-B * C} &&
\green{{}+-B * C} \\ \\
expr(["*", A + B * D, X]) &=& E - B * C
\end{eqnarray}
Divide both sides by
\green{A + B * D}
to isolate X:
\qquad\begin{eqnarray}
\green{A + B * D}X &=&
E - B * C \\ \\
\dfrac{\green{\cancel{A + B * D}}
X}{\green{\cancel{A + B * D}}}
&=& \dfrac{E - B * C}
{\green{A + B * D}} \\ \\
\end{eqnarray}
Simplify:
\qquad
X = fractionReduce(E - B * C, A + B * D)
Solve for X:
\qquad
expr(["*", A, ["+", ["*", B, X], C]]) =
expr(["+", ["*", D, X], E])
X =
SOLUTION
Try simplifying the left side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{A}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{A}:
\qquad\begin{eqnarray}
\pink{A}\blue{(expr(["+", ["*", B, X], C]))} &=&
expr(["+", ["*", D, X], E]) \\ \\
\pink{(A)}\blue{(expr(["*", B, X]))} +
\pink{(A)}\blue{(C)} &=&
expr(["+", ["*", D, X], E])
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A * B, X], A * C]) =
expr(["+", ["*", D, X], E])
Add
\green{expr(["*", abs(D), X])}
to both
sides to eliminate the X term
from the right side:
Subtract
\green{expr(["*", abs(D), X])}
from both
sides to eliminate the X term
from the right side:
\qquad\begin{eqnarray}
expr(["+", ["*", A * B, X], A * C]) &=&
\green{expr(["*", D, X])} + E \\ \\
\green{{}+expr(["*", -D, X])}
&& \green{{} +
expr(["*", -D, X])} \\ \\
expr(["+", ["*", A * B, X], A * C])
\green{{} + expr(["*", -D, X])} &=&
E
\end{eqnarray}
Combine the
X terms:
\qquad\begin{eqnarray}
\blue{expr(["*", A * B, X])} + A * C
\blue{{}+ expr(["*", -D, X])}
&=& E \\ \\
\blue{expr(["*", A * B - D, X])} + A * C &=& E
\end{eqnarray}
Add
\green{abs(A * C)}
to both sides
to isolate the X term on the
left side:
Subtract
\green{abs(A * C)}
from both sides
to isolate the X term on the
left side:
\qquad\begin{eqnarray}
expr(["*", A * B - D, X]) \green{{} + A * C} &=& E \\ \\
\green{{}+-A * C} &&
\green{{}+-A * C} \\ \\
expr(["*", A * B - D, X]) &=& E - A * C
\end{eqnarray}
Divide both sides by
\green{A * B - D}
to isolate X:
\qquad\begin{eqnarray}
\green{A * B - D}X &=&
E - A * C \\ \\
\dfrac{\green{\cancel{A * B - D}}
X}{\green{\cancel{A * B - D}}}
&=& \dfrac{E - A * C}
{\green{A * B - D}} \\ \\
\end{eqnarray}
Simplify:
\qquad
X = fractionReduce(E - A * C, A * B - D)
Solve for X:
\qquad
expr(["+", ["*", A, ["+", ["*", B, X], C]], D]) =
expr(["+", E, ["*", F, X]])
X =
SOLUTION
Try simplifying the left side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{A}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{A}:
\qquad\begin{eqnarray}
\pink{A}\blue{(expr(["+", ["*", B, X], C]))} + D &=&
expr(["+", E, ["*", F, X]]) \\ \\
\pink{(A)}\blue{(expr(["*", B, X]))} +
\pink{(A)}\blue{(C)} + D &=&
expr(["+", E, ["*", F, X]])
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A * B, X], A * C, D]) =
expr(["+", E, ["*", F, X]])
Add
\green{expr(["*", abs(F), X])}
to both
sides to eliminate the X term
from the right side:
Subtract
\green{expr(["*", abs(F), X])}
from both
sides to eliminate the X term
from the right side:
\qquad\begin{eqnarray}
expr(["+", ["*", A * B, X], A * C, D]) &=&
E \green{{} + expr(["*", F, X])} \\ \\
\green{{}+expr(["*", -F, X])}
&& \green{{} +
expr(["*", -F, X])} \\ \\
expr(["+", ["*", A * B, X], A * C, D])
\green{{}+expr(["*", -F, X])} &=&
E
\end{eqnarray}
Combine the
X terms:
\qquad\begin{eqnarray}
\blue{expr(["*", A * B, X])} +
expr(["+", A * C, D])
\blue{{} + expr(["*", -F, X])} &=& E \\ \\
expr(["+", A * C, D])
\blue{{} + expr(["*", A * B - F, X])} &=& E
\end{eqnarray}
Combine the numeric terms:
\qquad\begin{eqnarray}
\blue{expr(["+", A * C, D])} +
expr(["*", A * B - F, X]) &=& E \\ \\
\blue{A * C + D} +
expr(["*", A * B - F, X]) &=& E
\end{eqnarray}
Add
\green{abs(A * C + D)}
to both sides
to isolate the X term on the
left side:
Subtract
\green{abs(A * C + D)}
from both sides
to isolate the X term on the
left side:
\qquad\begin{eqnarray}
\green{A * C + D} + expr(["*", A * B - F, X]) &=& E \\ \\
\green{{}+-(A * C + D)} &&
\green{{}+-(A * C + D)} \\ \\
expr(["*", A * B - F, X]) &=& E - A * C - D
\end{eqnarray}
Divide both sides by
\green{A * B - F}
to isolate X:
\qquad\begin{eqnarray}
\green{A * B - F}X &=&
E - A * C - D \\ \\
\dfrac{\green{\cancel{A * B - F}}
X}{\green{\cancel{A * B - F}}}
&=& \dfrac{E - A * C - D}
{\green{A * B - F}} \\ \\
\end{eqnarray}
Simplify:
\qquad
X = fractionReduce(E - A * C - D, A * B - F)
Solve for X:
\qquad
expr(["*", A, ["+", ["*", B, X], C]]) =
expr(["*", D, ["+", E, ["*", F, X]]])
X =
SOLUTION
Try simplifying each side of the equation before solving it.
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{A}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{A}:
\qquad\begin{eqnarray}
\pink{A}\blue{(expr(["+", ["*", B, X], C]))} &=&
expr(["*", D, ["+", E, ["*", F, X]]]) \\ \\
\pink{(A)}\blue{(expr(["*", B, X]))} +
\pink{(A)}\blue{(C)} &=&
expr(["*", D, ["+", E, ["*", F, X]]])
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A * B, X], A * C]) =
expr(["*", D, ["+", E, ["*", F, X]]])
Distribute the negative in front of the parentheses.
Be careful! The negative sign in front of the
parentheses means we're multiplying by
\pink{-1}:
Distribute the \pink{D}.
Be careful to pay attention to the negative sign
when you distribute:
Distribute the \pink{D}:
\qquad\begin{eqnarray}
expr(["+", ["*", A * B, X], A * C]) &=&
\pink{(D)}\blue{(expr(["+", E, ["*", F, X]]))} \\ \\
expr(["+", ["*", A * B, X], A * C]) &=&
\pink{(D)} \blue{(E)} +
\pink{(D)}
\blue{(expr(["*", F, X]))}
\end{eqnarray}
Multiply:
\qquad
expr(["+", ["*", A * B, X], A * C]) =
expr(["+", D * E, ["*", D * F, X]])
Add
\green{expr(["*", abs(D * F), X])}
to both
sides to eliminate the X term
from the right side:
Subtract
\green{expr(["*", abs(D * F), X])}
from both
sides to eliminate the X term
from the right side:
\qquad\begin{eqnarray}
expr(["+", ["*", A * B, X], A * C]) &=&
D * E \green{{} + expr(["*", D * F, X])} \\ \\
\green{{}+expr(["*", -(D * F), X])}
&& \green{{} +
expr(["*", -(D * F), X])} \\ \\
expr(["+", ["*", A * B, X], A * C])
\green{+expr(["*", -(D * F), X])} &=&
D * E
\end{eqnarray}
Combine the
X terms:
\qquad\begin{eqnarray}
\blue{expr(["*", A * B, X])} + A * C
\blue{+expr(["*", -(D * F), X])} &=&
D * E \\ \\
\blue{expr(["*", A * B - D * F, X])} + A * C &=&
D * E
\end{eqnarray}
Add
\green{abs(A * C)}
to both sides
to isolate the X term on the
left side:
Subtract
\green{abs(A * C)}
from both sides
to isolate the X term on the
left side:
\qquad\begin{eqnarray}
expr(["*", A * B - D * F, X]) + \green{A * C} &=&
D * E \\ \\
\green{{}+-A * C} &&
\green{{}+-A * C} \\ \\
expr(["*", A * B - D * F, X])
&=& D * E - A * C
\end{eqnarray}
Divide both sides by
\green{A * B - D * F}
to isolate X:
\qquad\begin{eqnarray}
expr(["*", A * B - D * F, X])
&=& D * E - A * C \\ \\
\dfrac{\green{\cancel{A * B - D * F}}
X}{\green{\cancel{A * B - D * F}}}
&=& \dfrac{D * E - A * C}
{\green{A * B - D * F}} \\ \\
\end{eqnarray}
Simplify:
\qquad
X
= fractionReduce(D * E - A * C, A * B - D * F)