Question

solve the following equation. check your solution.
-2(3s - 2) - 4 = -3(4s + 5) - 5

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is s = \square. (simplify your answer.)
b. the solution is all real numbers.
c. there is no solution.

Explanation:

Step1: Expand both sides

Left side: $-2(3s - 2) - 4 = -6s + 4 - 4 = -6s$
Right side: $-3(4s + 5) - 5 = -12s - 15 - 5 = -12s - 20$

Step2: Solve for s

Set the expanded expressions equal: $-6s = -12s - 20$
Add $12s$ to both sides: $-6s + 12s = -20$
Simplify: $6s = -20$
Divide by 6: $s = \frac{-20}{6} = -\frac{10}{3}$

Step3: Check the solution

Substitute $s = -\frac{10}{3}$ into original equation:
Left: $-2(3(-\frac{10}{3}) - 2) - 4 = -2(-10 - 2) - 4 = -2(-12) - 4 = 24 - 4 = 20$
Right: $-3(4(-\frac{10}{3}) + 5) - 5 = -3(-\frac{40}{3} + 5) - 5 = -3(-\frac{40}{3} + \frac{15}{3}) - 5 = -3(-\frac{25}{3}) - 5 = 25 - 5 = 20$
Left = Right, so solution is valid.

Answer:

A. The solution is $s = -\frac{10}{3}$.