Solve for X:
\qquad
A1 = B1 + coefficient(C1)\left(D1 + E1\right)
B1 + coefficient(C1)\left(E1 + D1\right) = A1
X = SOLUTION
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{fractionReduce(C, C_DENOM)}:
\qquad\begin{eqnarray}
A1 &=& B1 + \pink{C1} \blue{\left(D1 + E1\right)} \\ \\
A1 &=& B1 +
\pink{\left(C1\right)}\blue{\left(D1\right)} +
\pink{\left(C1\right)}\blue{\left(E1\right)} \\ \\
A1 &=& B1 + CD + CE
\end{eqnarray}
\qquad\begin{eqnarray}
B1 + \pink{C1} \blue{\left(E1 + D1\right)} &=& A1 \\ \\
B1 +
\pink{\left(C1\right)}\blue{\left(E1\right)} +
\pink{\left(C1\right)}\blue{\left(D1\right)} &=& A1 \\ \\
B1 + CE + CD &=& A1
\end{eqnarray}
Combine the X terms:
\qquad\begin{eqnarray}
A1 &=& \blue{B1 + CD} + CE \\ \\
A1 &=&
\blue{\dfrac{coefficient(B / B_GCD)X + coefficient((C * D) / D_GCD)X}
{B_DENOM / D_GCD}} + CE \\ \\
A1 &=&
\blue{\dfrac{coefficient((B / B_GCD) + (C * D) / D_GCD)X}
{B_DENOM / D_GCD}} + CE \\ \\
A1 &=& \blue{coefficient(BD)X} + CE
\end{eqnarray}
\qquad\begin{eqnarray}
\blue{B1} + CE + \blue{CD} &=& A1 \\ \\
\blue{\dfrac{coefficient(B / B_GCD)X + coefficient((C * D) / D_GCD)X}
{B_DENOM / D_GCD}} + CE &=& A1 \\ \\
\blue{\dfrac{coefficient((B / B_GCD) + (C * D) / D_GCD)X}
{B_DENOM / D_GCD}} + CE &=& A1 \\ \\
\blue{coefficient(BD)X} + CE &=& A1
\end{eqnarray}
Add \purple{fractionReduce(-C * E, A_DENOM)} to both sides:
Subtract \purple{CE} from both sides:
\qquad\begin{eqnarray}
A1 + \purple{fractionReduce(-C * E, A_DENOM)} &=& coefficient(BD)X \\ \\
\dfrac{A / A_GCD + \purple{(-C * E) / E_GCD}}
{A_DENOM / E_GCD} &=& coefficient(BD)X \\ \\
\dfrac{(A - C * E) / E_GCD}{A_DENOM / E_GCD} &=& coefficient(BD)X \\ \\
AE &=& coefficient(BD)X
\end{eqnarray}
\qquad\begin{eqnarray}
coefficient(BD)X &=& A1 + \purple{fractionReduce(-C * E, A_DENOM)} \\ \\
coefficient(BD)X &=&
\dfrac{A / A_GCD + \purple{(-C * E) / E_GCD}}{A_DENOM / E_GCD} \\ \\
coefficient(BD)X &=& \dfrac{(A - C * E) / E_GCD}{A_DENOM / E_GCD} \\ \\
coefficient(BD)X &=& AE
\end{eqnarray}
Divide both sides by \green{BD} to isolate X:
\qquad
\dfrac{AE}{\green{BD}} =
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}}
\qquad
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}} =
\dfrac{AE}{\green{BD}}
\qquad X = fractionReduce(SOL_NUM, SOL_DEN)
\qquad
A1 - B1 = coefficient(C1)\left(D1 + E1\right)
coefficient(C1)\left(E1 + D1\right) = A1 - B1
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{fractionReduce(C, C_DENOM)}:
\qquad\begin{eqnarray}
A1 - B1 &=& \pink{C1} \blue{\left(D1 + E1\right)} \\ \\
A1 - B1 &=&
\pink{\left(C1\right)}\blue{\left(D1\right)} +
\pink{\left(C1\right)}\blue{\left(E1\right)} \\ \\
A1 - B1 &=& CD + CE
\end{eqnarray}
\qquad\begin{eqnarray}
\pink{C1} \blue{\left(E1 + D1\right)} &=& A1 - B1 \\ \\
\pink{\left(C1\right)}\blue{\left(E1\right)} +
\pink{\left(C1\right)}\blue{\left(D1\right)} &=& A1 - B1 \\ \\
CE + CD &=& A1 - B1
\end{eqnarray}
Add \blue{B1} to both sides:
Subtract \blue{fractionVariable(-B, B_DENOM, X)} from both sides:
\qquad\begin{eqnarray}
A1 &=& \blue{B1} + CD + CE \\ \\
A1 &=&
\dfrac{\blue{coefficient(B / B_GCD)X} + coefficient((C * D) / D_GCD)X}
{B_DENOM / D_GCD} + CE \\ \\
A1 &=&
\dfrac{coefficient((B / B_GCD) + (C * D) / D_GCD)X}
{B_DENOM / D_GCD} + CE \\ \\
A1 &=& coefficient(BD)X + CE
\end{eqnarray}
\qquad\begin{eqnarray}
\blue{B1} + CE + CD &=& A1 \\ \\
\dfrac{\blue{coefficient(B / B_GCD)X} + coefficient((C * D) / D_GCD)X}
{B_DENOM / D_GCD} + CE &=& A1 \\ \\
\dfrac{coefficient((B / B_GCD) + (C * D) / D_GCD)X}
{B_DENOM / D_GCD} + CE &=& A1 \\ \\
\blue{coefficient(BD)X} + CE &=& A1
\end{eqnarray}
Add \purple{fractionReduce(-C * E, A_DENOM)} to both sides:
Subtract \purple{CE} from both sides:
\qquad\begin{eqnarray}
A1 + \purple{fractionReduce(-C * E, A_DENOM)} &=& coefficient(BD)X \\ \\
\dfrac{A / A_GCD + \purple{(-C * E) / E_GCD}}
{A_DENOM / E_GCD} &=& coefficient(BD)X \\ \\
\dfrac{(A - C * E) / E_GCD}{A_DENOM / E_GCD} &=& coefficient(BD)X \\ \\
AE &=& coefficient(BD)X
\end{eqnarray}
\qquad\begin{eqnarray}
coefficient(BD)X &=& A1 + \purple{fractionReduce(-C * E, A_DENOM)} \\ \\
coefficient(BD)X &=&
\dfrac{A / A_GCD + \purple{(-C * E) / E_GCD}}{A_DENOM / E_GCD} \\ \\
coefficient(BD)X &=& \dfrac{(A - C * E) / E_GCD}{A_DENOM / E_GCD} \\ \\
coefficient(BD)X &=& AE
\end{eqnarray}
Divide both sides by \green{BD} to isolate X:
\qquad
\dfrac{AE}{\green{BD}} =
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}}
\qquad
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}} =
\dfrac{AE}{\green{BD}}
\qquad X = fractionReduce(SOL_NUM, SOL_DEN)
Solve for X:
\qquad
A = BX + CC(DX + E)
BX + CC(E + DX) = A
X = SOLUTION
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}:
\qquad\begin{eqnarray}
A &=& BX + \pink{C}\blue{(DX + E)} \\ \\
A &=& BX + \pink{(C)}\blue{(DX)} +
\pink{(C)}\blue{(E)} \\ \\
A &=& BX + CDX + CE
\end{eqnarray}
\qquad\begin{eqnarray}
BX + \pink{C} \blue{(E + DX)} &=& A \\ \\
BX + \pink{(C)}\blue{(E)} + \pink{(C)}\blue{(DX)}
&=& A \\ \\
BX + CE + CDX &=& A
\end{eqnarray}
Combine the X terms:
\qquad\begin{eqnarray}
A &=& \blue{BX + CDX} + CE \\ \\
A &=& \blue{BDX} + CE
\end{eqnarray}
\qquad\begin{eqnarray}
\blue{BX} + CE + \blue{CDX} &=& A \\ \\
\blue{BDX} + CE &=& A
\end{eqnarray}
Add \purple{roundTo(2, -C * E)} to both sides:
Subtract \purple{CE} from both sides:
\qquad\begin{eqnarray}
A + \purple{roundTo(2, -C * E)} &=& BDX \\ \\
roundTo(4, SOL_NUM * MULTIPLE) &=& BDX
\end{eqnarray}
\qquad\begin{eqnarray}
BDX &=& A + \purple{roundTo(2, -C * E)} \\ \\
BDX &=& roundTo(4, SOL_NUM * MULTIPLE)
\end{eqnarray}
Divide both sides by \green{BD} to isolate X:
\qquad
\dfrac{roundTo(4, SOL_NUM * MULTIPLE)}{\green{BD}} =
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}}
\qquad
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}} =
\dfrac{roundTo(4, SOL_NUM * MULTIPLE)}{\green{BD}}
\qquad X = fractionReduce(SOL_NUM, SOL_DEN)
Solve for X:
\qquad
A - BX = CC(DX + E)
CC(E + DX) = A - BX
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}:
\qquad\begin{eqnarray}
A - BX &=& \pink{C}\blue{(DX + E)} \\ \\
A - BX &=& \pink{(C)}\blue{(DX)} +
\pink{(C)}\blue{(E)} \\ \\
A - BX &=& CDX + CE
\end{eqnarray}
\qquad\begin{eqnarray}
\pink{C} \blue{(E + DX)} &=& A \\ \\
\pink{(C)}\blue{(E)} + \pink{(C)}\blue{(DX)} &=&
A - BX \\ \\
CE + CDX &=& A - BX
\end{eqnarray}
Add \purple{BX} to both sides:
Subtract \purple{coefficient(-B) + X} from both sides:
\qquad\begin{eqnarray}
A &=& CDX + CE + \purple{BX} \\ \\
A &=& BDX + CE
\end{eqnarray}
\qquad\begin{eqnarray}
CE + CDX + \purple{BX} &=& A\\ \\
CE + BDX &=& A
\end{eqnarray}
Add \purple{roundTo(2, -C * E)} to both sides:
Subtract \purple{CE} from both sides:
\qquad\begin{eqnarray}
A + \purple{roundTo(2, -C * E)} &=& BDX \\ \\
roundTo(4, SOL_NUM * MULTIPLE) &=& BDX
\end{eqnarray}
\qquad\begin{eqnarray}
BDX &=& A + \purple{roundTo(2, -C * E)} \\ \\
BDX &=& roundTo(4, SOL_NUM * MULTIPLE)
\end{eqnarray}
Divide both sides by \green{BD} to isolate X:
\qquad
\dfrac{roundTo(4, SOL_NUM * MULTIPLE)}{\green{BD}} =
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}}
\qquad
\dfrac{\green{\cancel{BD}}X}{\green{\cancel{BD}}} =
\dfrac{roundTo(4, SOL_NUM * MULTIPLE)}{\green{BD}}
\qquad X = fractionReduce(SOL_NUM, SOL_DEN)
Solve for X:
\qquad
A1 - B1 = F1 + coefficient(C1)\left(D1 + E1\right)
F1 + coefficient(C1)\left(E1 + D1\right) = A1 - B1
X = SOLUTION
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{fractionReduce(C, C_DENOM)}:
\qquad\begin{eqnarray}
A1 - B1 &=&
F1 + \pink{C1} \blue{\left(D1 + E1\right)} \\ \\
A1 - B1 &=&
F1 +
\pink{\left(C1\right)}\blue{\left(D1\right)} +
\pink{\left(C1\right)}\blue{\left(E1\right)} \\ \\
A1 - B1 &=&
F1 + fractionVariable(C * D, B_DENOM, X) + fractionReduce(C * E, A_DENOM)
\end{eqnarray}
\qquad\begin{eqnarray}
F1 + \pink{C1} \blue{\left(E1 + D1\right)} &=&
A1 - B1 \\ \\
F1 +
\pink{\left(C1\right)}\blue{\left(E1\right)} +
\pink{\left(C1\right)}\blue{\left(D1\right)} &=&
A1 - B1 \\ \\
F1 + fractionReduce(C * E, A_DENOM) + fractionVariable(C * D, B_DENOM, X) &=&
A1 - B1
\end{eqnarray}
Multiply each term by a common denominator of COMMON_DENOM
\qquad A2 - B2 = F2 + CD2 + CE2
\qquad F2 + CE2 + CD2 = A2 - B2
Add \blue{B2} to both sides:
Subtract \blue{fractionVariable(-B * COMMON_DENOM, B_DENOM, X)} from both sides:
\qquad A2 = F2 + CD2 + CE2 + \blue{B2}
\qquad F2 + CE2 + CD2 + \blue{B2} = A2
Combine the X terms:
\qquad\begin{eqnarray}
A2 &=& \blue{F2 + CD2} + CE2 + \blue{B2} \\ \\
A2 &=& \blue{FBDX} + CE2
\end{eqnarray}
\qquad\begin{eqnarray}
\blue{F2} + CE2 + \blue{CD2 + B2} &=& A2 \\ \\
\blue{FBDX} + CE2 &=& A2
\end{eqnarray}
Add \purple{-CE2} to both sides:
Subtract \purple{CE2} from both sides:
\qquad\begin{eqnarray}
A2 + \purple{-CE2} &=& FBDX \\ \\
AE &=& FBDX
\end{eqnarray}
\qquad\begin{eqnarray}
FBDX &=& A2 + \purple{-CE2} \\ \\
FBDX &=& AE
\end{eqnarray}
Divide both sides by \green{FBD} to isolate X:
\qquad
\dfrac{AE}{\green{FBD}} =
\dfrac{\green{\cancel{FBD}}X}{\green{\cancel{FBD}}}
\qquad
\dfrac{\green{\cancel{FBD}}X}{\green{\cancel{FBD}}} =
\dfrac{AE}{\green{FBD}}
\qquad X = fractionReduce(SOL_NUM, SOL_DEN)
Solve for X:
\qquad
A - BX = FX + CC(DX + E)
FX + CC(E + DX) = A - BX
X = SOLUTION
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}:
\qquad\begin{eqnarray}
A - BX &=& FX + \pink{C}\blue{(DX + E)} \\ \\
A - BX &=& FX + \pink{(C)}\blue{(DX)} +
\pink{(C)}\blue{(E)} \\ \\
A - BX &=& FX + CDX + CE
\end{eqnarray}
\qquad\begin{eqnarray}
FX + \pink{C} \blue{(E + DX)} &=& A - BX \\ \\
FX + \pink{(C)}\blue{(E)} + \pink{(C)}\blue{(DX)}
&=& A - BX \\ \\
FX + CE + CDX &=& A - BX
\end{eqnarray}
Add \blue{BX} to both sides:
Subtract \blue{coefficient(-B) + X} from both sides:
\qquad
A = FX + CDX + CE + \blue{BX}
\qquad
FX + CE + CDX + \blue{BX} = A
Combine the X terms:
\qquad\begin{eqnarray}
A &=& \blue{FX + CDX} + CE + \blue{BX} \\ \\
A &=& \blue{BDFX} + CE
\end{eqnarray}
\qquad\begin{eqnarray}
\blue{FX} + CE + \blue{CDX + BX} &=& A \\ \\
\blue{BDFX} + CE &=& A
\end{eqnarray}
Add \purple{-CE} to both sides:
Subtract \purple{CE} from both sides:
\qquad\begin{eqnarray}
A + \purple{-CE} &=& BDFX \\ \\
roundTo(4, SOL_NUM * MULTIPLE) &=& BDFX
\end{eqnarray}
\qquad\begin{eqnarray}
BDFX &=& A + \purple{-CE} \\ \\
BDFX &=& roundTo(4, SOL_NUM * MULTIPLE)
\end{eqnarray}
Divide both sides by \green{BDF} to isolate X:
\qquad
\dfrac{roundTo(4, SOL_NUM * MULTIPLE)}{\green{BDF}} =
\dfrac{\green{\cancel{BDF}}X}{\green{\cancel{BDF}}}
\qquad
\dfrac{\green{\cancel{BDF}}X}{\green{\cancel{BDF}}} =
\dfrac{roundTo(4, SOL_NUM * MULTIPLE)}{\green{BDF}}
\qquad X = fractionReduce(SOL_NUM, SOL_DEN)