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?

1 answer

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