Question

Solve the equation. \(9=-\frac{3}{2}(x-2)\)

Short answer

The solution to the equation is \(x = -4\).

Step-by-step solution

Multiply the fraction by the term in brackets

The equation can be rewritten as \(9 = -\frac{3}{2}x +3\) by distributing the \(-\frac{3}{2}\) to both terms inside the brackets.

Isolate x term

Subtract 3 from both sides to get the equation \(-\frac{3}{2}x = 6\).

Solve for x

Divide both sides by -\frac{3}{2}. We can multiply the both sides by the reciprocal of -\frac{3}{2} which is -\frac{2}{3}. The solution for the equation would be \(x=-\frac{2}{3}*6=-4\).