Sure, let's solve the equation step-by-step and then verify the solution to ensure it's correct.
### Step-by-Step Solution
Given the equation:
[tex]\[ 2n - 7 = -31 \][/tex]
1. Isolate the term with [tex]\( n \)[/tex]:
To begin solving for [tex]\( n \)[/tex], we need to isolate the term with [tex]\( n \)[/tex]. We can do this by adding 7 to both sides of the equation:
[tex]\[
2n - 7 + 7 = -31 + 7
\][/tex]
2. Simplify:
Simplifying both sides of the equation, we get:
[tex]\[
2n = -24
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
Next, we need to isolate [tex]\( n \)[/tex]. We can do this by dividing both sides of the equation by 2:
[tex]\[
\frac{2n}{2} = \frac{-24}{2}
\][/tex]
4. Simplify the division:
Simplifying the division, we find:
[tex]\[
n = -12
\][/tex]
### Verification
To ensure our solution is correct, we can substitute the value of [tex]\( n \)[/tex] back into the original equation and see if both sides are equal.
Substitute [tex]\( n = -12 \)[/tex] into the original equation:
[tex]\[
2n - 7 = -31
\][/tex]
Calculate the left-hand side (LHS) with [tex]\( n = -12 \)[/tex]:
[tex]\[
2(-12) - 7 = -24 - 7 = -31
\][/tex]
The right-hand side (RHS) is already given as:
[tex]\[
-31
\][/tex]
Since the LHS equals the RHS:
[tex]\[
-31 = -31
\][/tex]
The solution is verified to be correct. Therefore, the value of [tex]\( n \)[/tex] is:
[tex]\[
n = -12
\][/tex]
