Answer :
To determine whether each number is a solution of the inequality [tex]\( 2x + 4 \geq -1 \)[/tex], we need to substitute each number into the inequality and verify if the inequality holds true.
### Part (a): Checking if [tex]\( 3 \)[/tex] is a solution.
1. Substitute [tex]\( 3 \)[/tex] for [tex]\( x \)[/tex] in the inequality:
[tex]\[ 2(3) + 4 \geq -1 \][/tex]
2. Simplify the expression:
[tex]\[ 6 + 4 \geq -1 \][/tex]
[tex]\[ 10 \geq -1 \][/tex]
Since [tex]\( 10 \geq -1 \)[/tex] is a true statement, [tex]\( 3 \)[/tex] is a solution to the inequality.
- Answer: Yes
### Part (b): Checking if [tex]\( -1 \)[/tex] is a solution.
1. Substitute [tex]\( -1 \)[/tex] for [tex]\( x \)[/tex] in the inequality:
[tex]\[ 2(-1) + 4 \geq -1 \][/tex]
2. Simplify the expression:
[tex]\[ -2 + 4 \geq -1 \][/tex]
[tex]\[ 2 \geq -1 \][/tex]
Since [tex]\( 2 \geq -1 \)[/tex] is a true statement, [tex]\( -1 \)[/tex] is a solution to the inequality.
- Answer: Yes
### Part (c): Checking if [tex]\( 1 \)[/tex] is a solution.
1. Substitute [tex]\( 1 \)[/tex] for [tex]\( x \)[/tex] in the inequality:
[tex]\[ 2(1) + 4 \geq -1 \][/tex]
2. Simplify the expression:
[tex]\[ 2 + 4 \geq -1 \][/tex]
[tex]\[ 6 \geq -1 \][/tex]
Since [tex]\( 6 \geq -1 \)[/tex] is a true statement, [tex]\( 1 \)[/tex] is a solution to the inequality.
- Answer: Yes
In conclusion:
- [tex]\( 3 \)[/tex] is a solution to the inequality.
- [tex]\( -1 \)[/tex] is a solution to the inequality.
- [tex]\( 1 \)[/tex] is a solution to the inequality.
### Part (a): Checking if [tex]\( 3 \)[/tex] is a solution.
1. Substitute [tex]\( 3 \)[/tex] for [tex]\( x \)[/tex] in the inequality:
[tex]\[ 2(3) + 4 \geq -1 \][/tex]
2. Simplify the expression:
[tex]\[ 6 + 4 \geq -1 \][/tex]
[tex]\[ 10 \geq -1 \][/tex]
Since [tex]\( 10 \geq -1 \)[/tex] is a true statement, [tex]\( 3 \)[/tex] is a solution to the inequality.
- Answer: Yes
### Part (b): Checking if [tex]\( -1 \)[/tex] is a solution.
1. Substitute [tex]\( -1 \)[/tex] for [tex]\( x \)[/tex] in the inequality:
[tex]\[ 2(-1) + 4 \geq -1 \][/tex]
2. Simplify the expression:
[tex]\[ -2 + 4 \geq -1 \][/tex]
[tex]\[ 2 \geq -1 \][/tex]
Since [tex]\( 2 \geq -1 \)[/tex] is a true statement, [tex]\( -1 \)[/tex] is a solution to the inequality.
- Answer: Yes
### Part (c): Checking if [tex]\( 1 \)[/tex] is a solution.
1. Substitute [tex]\( 1 \)[/tex] for [tex]\( x \)[/tex] in the inequality:
[tex]\[ 2(1) + 4 \geq -1 \][/tex]
2. Simplify the expression:
[tex]\[ 2 + 4 \geq -1 \][/tex]
[tex]\[ 6 \geq -1 \][/tex]
Since [tex]\( 6 \geq -1 \)[/tex] is a true statement, [tex]\( 1 \)[/tex] is a solution to the inequality.
- Answer: Yes
In conclusion:
- [tex]\( 3 \)[/tex] is a solution to the inequality.
- [tex]\( -1 \)[/tex] is a solution to the inequality.
- [tex]\( 1 \)[/tex] is a solution to the inequality.
