Question

Determine whether each number is a solution of the inequality below.
5 x plus 2greater than or equalsnegative 8
a. negative 2
b. negative 1
c. 3
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Part 1
a. Is negative 2 a​ solution?

Answer 1

To determine whether each number is a solution of the inequality \(5x + 2 \geq -8\), we can substitute each value into the inequality and check if it holds true.

Let's check the first value:

### a. \(x = -2\)

Substituting \(-2\) into the inequality:

\[
5(-2) + 2 \geq -8
\]

Calculating:

\[
-10 + 2 \geq -8
\]

\[
-8 \geq -8
\]

This statement is true.

So, **-2 is a solution of the inequality**.

### Now, let's check the other values.

### b. \(x = -1\)

Substituting \(-1\) into the inequality:

\[
5(-1) + 2 \geq -8
\]

Calculating:

\[
-5 + 2 \geq -8
\]

\[
-3 \geq -8
\]

This statement is also true.

So, **-1 is a solution of the inequality**.

### c. \(x = 3\)

Substituting \(3\) into the inequality:

\[
5(3) + 2 \geq -8
\]

Calculating:

\[
15 + 2 \geq -8
\]

\[
17 \geq -8
\]

This statement is true as well.

So, **3 is also a solution of the inequality**.

### Summary:
- a. \(-2\) is a solution: **Yes**
- b. \(-1\) is a solution: **Yes**
- c. \(3\) is a solution: **Yes**