Sure, let's solve the equation step-by-step:
Given equation:
[tex]\[ 7x - 6(x + 5) = 2x - 3 \][/tex]
Step 1: Distribute the [tex]\(-6\)[/tex] across [tex]\((x + 5)\)[/tex]:
[tex]\[
7x - 6x - 30 = 2x - 3
\][/tex]
Step 2: Combine like terms on the left side:
[tex]\[
x - 30 = 2x - 3
\][/tex]
Step 3: Isolate the variable term by subtracting [tex]\(2x\)[/tex] from both sides of the equation:
[tex]\[
x - 2x - 30 = -3
\][/tex]
[tex]\[
-x - 30 = -3
\][/tex]
Step 4: Solve for [tex]\(x\)[/tex] by adding 30 to both sides:
[tex]\[
-x = -3 + 30
\][/tex]
[tex]\[
-x = 27
\][/tex]
Step 5: Multiply both sides by [tex]\(-1\)[/tex] to find [tex]\(x\)[/tex]:
[tex]\[
x = -27
\][/tex]
Therefore, the solution set is [tex]\(\{-27\}\)[/tex].
Verification:
Substitute [tex]\( x = -27 \)[/tex] back into the original equation to verify:
Left side:
[tex]\[ 7(-27) - 6(-27 + 5) \][/tex]
[tex]\[ = -189 - 6(-22) \][/tex]
[tex]\[ = -189 + 132 \][/tex]
[tex]\[ = -57 \][/tex]
Right side:
[tex]\[ 2(-27) - 3 \][/tex]
[tex]\[ = -54 - 3 \][/tex]
[tex]\[ = -57 \][/tex]
Both sides match, confirming that:
[tex]\[ x = -27 \][/tex]
The correct choice is:
A. The solution set is [tex]\(\{-27\}\)[/tex].
