Question

solve the equation.
3(4 + 2x) = 5(x - 5)
select the correct choice below and fill in any answer boxes in your choice.
a. the solution set is { }. (type an integer or a simplified fraction.)
b. there is no solution.

Explanation:

Step1: Expand both sides

Expand the left - hand side: \(3(4 + 2x)=3\times4+3\times2x = 12 + 6x\)
Expand the right - hand side: \(5(x - 5)=5\times x-5\times5=5x - 25\)
So the equation becomes \(12 + 6x=5x - 25\)

Step2: Isolate the variable x

Subtract \(5x\) from both sides: \(12 + 6x-5x=5x - 25-5x\)
Simplify to get \(12 + x=-25\)
Then subtract 12 from both sides: \(x=-25 - 12\)
Calculate the right - hand side: \(x=-37\)

Answer:

A. The solution set is \(\{-37\}\)