Question

Which of the following values is a solution for the inequality statement?
Select all that apply.
-5 ≤ -4r + 3

0
3
-5
4
7

Answer 1

To determine which values satisfy the inequality \(-5 \leq -4r + 3\), we first need to isolate \(r\).

1. Start with the inequality:
\(-5 \leq -4r + 3\)

2. Subtract 3 from both sides:
\(-5 - 3 \leq -4r\)
\(-8 \leq -4r\)

3. Divide both sides by -4. Remember that when you divide by a negative number, the inequality sign flips:
\(\frac{-8}{-4} \geq r\)
\(2 \geq r\) or \(r \leq 2\)

Now we need to check which of the given values satisfy the condition \(r \leq 2\):

- For \(r = 0\):
\(0 \leq 2\) (True)

- For \(r = 3\):
\(3 \leq 2\) (False)

- For \(r = -5\):
\(-5 \leq 2\) (True)

- For \(r = 4\):
\(4 \leq 2\) (False)

- For \(r = 7\):
\(7 \leq 2\) (False)

The values that satisfy the inequality are:

- **0**
- **-5**

So the solutions are **0 and -5**.