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Five more than twice a number is greater than negative eleven. Solve the inequality for the unknown number.

Simplify your answer. Type an inequality using x as the variable.

\[ 2x + 5 > -11 \]

Answer :

Sure! Let's solve the inequality step-by-step for the unknown number [tex]\( x \)[/tex].

### Problem Statement:
Five more than twice a number is greater than negative eleven. We need to solve this inequality for [tex]\( x \)[/tex].

### Step-by-Step Solution:
1. Set up the inequality:
We begin by translating the given statement into a mathematical inequality.
[tex]\[
2x + 5 > -11
\][/tex]

2. Isolate the term containing [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to get rid of the constant term on the left side. We do this by subtracting 5 from both sides of the inequality.
[tex]\[
2x + 5 - 5 > -11 - 5
\][/tex]
Simplify both sides:
[tex]\[
2x > -16
\][/tex]

3. Solve for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to divide both sides of the inequality by 2.
[tex]\[
\frac{2x}{2} > \frac{-16}{2}
\][/tex]
Simplify both sides:
[tex]\[
x > -8
\][/tex]

### Final Answer:
The solution to the inequality is:
[tex]\[
x > -8
\][/tex]

So, in simple terms: any number greater than [tex]\(-8\)[/tex] will satisfy the given inequality.

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