randRange( 2, 8 ) randRangeNonZero( -12, 18 ) randRangeNonZero( -6, 6 ) randRangeNonZero( -6, 6 ) ( B - A * D ) / ( A * C )

Solve for x:

A = \dfrac{B}{expr(["*", C, "x"]) + D}

x = ANSWER

Multiply both sides by expr(["*", C, "x"]) + D:

\qquad A (expr(["*", C, "x"]) + D) = \dfrac{B}{expr(["*", C, "x"]) + D} (expr(["*", C, "x"]) + D)

\qquad A * Cx + A * D = B

Now A * D < 0 ? "add" : "subtract" abs( A * D ) A * D < 0 ? "to" : "from" both sides:

\qquad (A * Cx + A * D) + -A * D = B + - A * D

\qquad A * Cx = B - A * D

Divide by A * C:

\qquad x = fraction( B - A * D, A * C, false, false )

Reduce the fraction:

\qquad x = fractionReduce( B - A * D, A * C )

randRangeNonZero( -12, 18 ) randRangeNonZero( -12, 18 ) randRangeNonZero( -6, 6 ) randRangeNonZero( -6, 6 ) randRange( 2, 8 ) ( E * D - B ) / ( A - E * C )

Solve for x:

\dfrac{expr(["*", A, "x"]) + B}{expr(["*", C, "x"]) + D} = E

x = ANSWER

Multiply both sides by expr(["*", C, "x"]) + D:

\qquad \dfrac{expr(["*", A, "x"]) + B}{expr(["*", C, "x"]) + D} (expr(["*", C, "x"]) + D) = E (expr(["*", C, "x"]) + D)

\qquad expr(["*", A, "x"]) + B = expr(["*", E * C, "x"]) + E * D

Now E * C < 0 ? "add" : "subtract" abs( E * C )x E * C < 0 ? "to" : "from" both sides:

\qquad (expr(["*", A, "x"]) + B) + -E * Cx = (expr(["*", E * C, "x"]) + E * D) + -E * Cx

\qquad A - E * Cx + B = E * D

Now B < 0 ? "add" : "subtract" abs( B ):

\qquad (A - E * Cx + B) + -B = E * D + -B

\qquad A - E * Cx = E * D - B

Divide by A - E * C:

\qquad x = fraction( E * D - B, A - E * C, false, false )

Reduce the fraction:

\qquad x = fractionReduce( E * D - B, A - E * C )