Question

Consider the equation

2/3(12 – Ax) – 4 = 9(6 x + B).
What values for A and B will result in an equation that has infinite solutions?

Answer 1

A = -81

B = 4/9

Explanation:

An equation that has infinite solutions suggests that the left side equals the right side.

Expand brackets:

`\frac23(12-Ax)-4 = 9(6 x + B)`

`\implies 4-\frac23Ax = 54x+9B`

Equate coefficients of x:

`\implies -\frac23A=54`

`\implies A=-81`

Equate constants:

`\implies 4=9B`

`\implies B=\frac49`