Let's solve the equation step-by-step:
The given equation is:
[tex]\[ 6y - 8 = 9y + 7 \][/tex]
Step 1: Isolate the variable [tex]\( y \)[/tex]. Start by moving all the [tex]\( y \)[/tex]-terms to one side and constant terms to the other side. Subtract [tex]\( 6y \)[/tex] from both sides:
[tex]\[ 6y - 8 - 6y = 9y + 7 - 6y \][/tex]
This simplifies to:
[tex]\[ -8 = 3y + 7 \][/tex]
Step 2: Next, isolate [tex]\( 3y \)[/tex] by subtracting 7 from both sides:
[tex]\[ -8 - 7 = 3y + 7 - 7 \][/tex]
This simplifies to:
[tex]\[ -15 = 3y \][/tex]
Step 3: Finally, solve for [tex]\( y \)[/tex] by dividing both sides by 3:
[tex]\[ y = \frac{-15}{3} \][/tex]
[tex]\[ y = -5 \][/tex]
So, the proposed solution is [tex]\( y = -5 \)[/tex].
Step 4: Verify the solution by substituting [tex]\( y = -5 \)[/tex] back into the original equation:
[tex]\[ 6y - 8 = 9y + 7 \][/tex]
Substitute [tex]\( y = -5 \)[/tex]:
[tex]\[ 6(-5) - 8 \stackrel{?}{=} 9(-5) + 7 \][/tex]
[tex]\[ -30 - 8 \stackrel{?}{=} -45 + 7 \][/tex]
[tex]\[ -38 = -38 \][/tex]
The left-hand side equals the right-hand side when [tex]\( y = -5 \)[/tex], so the solution [tex]\( y = -5 \)[/tex] checks out.
Therefore, the solution set is:
[tex]\[ \{-5\} \][/tex]
Hence, the correct choice is:
A. The solution set is \{-5\}.
