Question

solve the equation and check your solution
-(7y + 5) - (-6y - 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

First, we distribute the negative signs in the equation \(-(7y + 5)-(-6y - 7)=0\).
Using the distributive property \(a(b + c)=ab+ac\), we have:
\(-7y-5 + 6y + 7 = 0\)

Step2: Combine like terms

Next, we combine the like terms. The like terms for \(y\) are \(-7y\) and \(6y\), and the constant terms are \(-5\) and \(7\).
Combining the \(y\) terms: \(-7y+6y=-y\)
Combining the constant terms: \(-5 + 7 = 2\)
So the equation becomes \(-y+2 = 0\)

Step3: Solve for \(y\)

We want to isolate \(y\). Subtract 2 from both sides of the equation \(-y+2 = 0\):
\(-y+2-2=0 - 2\)
\(-y=-2\)
Multiply both sides by \(- 1\) to solve for \(y\):
\(y = 2\)

Step4: Check the solution

Now we check the solution by substituting \(y = 2\) back into the original equation.
Left - hand side: \(-(7(2)+5)-(-6(2)-7)\)
First, calculate inside the parentheses:
\(7(2)+5=14 + 5=19\) and \(-6(2)-7=-12-7=-19\)
Then, \(-(19)-(-19)=-19 + 19=0\)
Which is equal to the right - hand side (which is 0). So the solution is correct.

Answer:

A. The solution set is \(\{2\}\)