Question

solve.
-5(6 - x) + 6 = 10 - 7(x + 2)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is x = \square. (type an integer or a simplified fraction.)
b. the solution is all real numbers.
c. there is no solution.

Explanation:

Step1: Expand both sides

First, we expand the left - hand side: \(-5(6 - x)+6=-30 + 5x+6=5x-24\)
Then, we expand the right - hand side: \(10-7(x + 2)=10-7x-14=-7x - 4\)
So the equation becomes \(5x-24=-7x - 4\)

Step2: Move terms with x to one side

Add \(7x\) to both sides of the equation: \(5x+7x-24=-7x + 7x-4\), which simplifies to \(12x-24=-4\)

Step3: Solve for x

Add 24 to both sides: \(12x-24 + 24=-4 + 24\), so \(12x=20\)
Divide both sides by 12: \(x=\frac{20}{12}=\frac{5}{3}\)

Answer:

A. The solution is \(x = \frac{5}{3}\)