To solve the equation [tex]\(x - 76 = 102\)[/tex], follow these steps:
1. Identify the original equation:
[tex]\[
x - 76 = 102
\][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
We need to move the constant term on the left side (which is -76) to the right side. To do this, we'll use the inverse operation of subtraction, which is addition. So, we'll add 76 to both sides of the equation to keep it balanced.
[tex]\[
x - 76 + 76 = 102 + 76
\][/tex]
3. Simplify the equation:
The -76 and +76 on the left side cancel each other out, leaving us with:
[tex]\[
x = 102 + 76
\][/tex]
4. Perform the addition:
[tex]\[
x = 178
\][/tex]
Thus, the solution to the equation [tex]\(x - 76 = 102\)[/tex] is:
[tex]\(\boxed{178}\)[/tex]
From the given options, the correct value for [tex]\(x\)[/tex] is [tex]\(178\)[/tex].
