Question

solve the equation and check your solution.
-(8y + 5) - (-7y - 7) = 0

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (simplify your answer.)
b. the solution set is {all real numbers}.
c. the solution set is ∅.

Explanation:

Step1: Distribute the negative signs

$-8y - 5 + 7y + 7 = 0$

Step2: Combine like terms

$(-8y + 7y) + (-5 + 7) = 0$
$\implies -y + 2 = 0$

Step3: Isolate the variable $y$

$-y = -2$
$\implies y = 2$

Step4: Verify the solution

Substitute $y=2$ into original equation:
$-(8(2)+5)-(-7(2)-7) = -(16+5)-(-14-7) = -21 - (-21) = -21 +21 = 0$
The left side equals the right side, so the solution is valid.

Answer:

A. The solution set is $\{2\}$.