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