Sure, let's solve the equation step by step:
Given the equation:
[tex]\[
\frac{x}{6} - 5 = -2
\][/tex]
1. Isolate the term with [tex]\(x\)[/tex] on one side of the equation:
We want to get [tex]\(\frac{x}{6}\)[/tex] by itself on the left side of the equation. To do this, we'll add 5 to both sides to cancel out the -5.
[tex]\[
\frac{x}{6} - 5 + 5 = -2 + 5
\][/tex]
Simplifying the equation:
[tex]\[
\frac{x}{6} = 3
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now, we need to isolate [tex]\(x\)[/tex]. Since [tex]\(x\)[/tex] is currently divided by 6, we can multiply both sides of the equation by 6.
[tex]\[
6 \cdot \frac{x}{6} = 3 \cdot 6
\][/tex]
On the left side, multiplying [tex]\(\frac{x}{6}\)[/tex] by 6 cancels out the division, leaving us with [tex]\(x\)[/tex]:
[tex]\[
x = 18
\][/tex]
So, the solution to the equation [tex]\(\frac{x}{6} - 5 = -2\)[/tex] is:
[tex]\[
x = 18
\][/tex]
