To determine which of the given solutions make the inequality [tex]\(2x - 1 \leq 5x + 20\)[/tex] true, we need to solve the inequality step-by-step and then check each provided value.
### Step 1: Solve the Inequality
Starting with the inequality:
[tex]\[ 2x - 1 \leq 5x + 20 \][/tex]
1. Subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[ -1 \leq 3x + 20 \][/tex]
2. Subtract 20 from both sides:
[tex]\[ -1 - 20 \leq 3x \][/tex]
[tex]\[ -21 \leq 3x \][/tex]
3. Divide both sides by 3:
[tex]\[ -7 \leq x \][/tex]
This simplifies to:
[tex]\[ x \geq -7 \][/tex]
### Step 2: Verify Each Provided Solution
We need to check if each given value of [tex]\(x\)[/tex] satisfies [tex]\(x \geq -7\)[/tex].
1. 10:
[tex]\[ 10 \geq -7 \][/tex]
True
2. -5:
[tex]\[ -5 \geq -7 \][/tex]
True
3. -20:
[tex]\[ -20 \geq -7 \][/tex]
False
4. -7:
[tex]\[ -7 \geq -7 \][/tex]
True
5. -60:
[tex]\[ -60 \geq -7 \][/tex]
False
6. 0:
[tex]\[ 0 \geq -7 \][/tex]
True
7. -9:
[tex]\[ -9 \geq -7 \][/tex]
False
### Solutions that make the inequality true:
- 10
- -5
- -7
- 0
Therefore, the values that satisfy the inequality [tex]\(2x - 1 \leq 5x + 20\)[/tex] are:
[tex]\[ 10, -5, -7, \text{ and } 0. \][/tex]
