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When the value of r is 23, the equation 3r−47.5=21.5 is a true statement. Which of the following values of r makes the inequality 3r−47.5>21.5 a true statement? (1 point)

Responses

22.5
22.5

22
22

23
23

23.5

3 answers

To solve the inequality \( 3r - 47.5 > 21.5 \), we will first solve for \( r \):

  1. Add 47.5 to both sides: \[ 3r > 21.5 + 47.5 \] \[ 3r > 69 \]

  2. Divide both sides by 3: \[ r > 23 \]

This means that any value of \( r \) that is greater than 23 will satisfy the inequality \( 3r - 47.5 > 21.5 \).

Among the given options:

  • 22.5 (not greater than 23)
  • 22 (not greater than 23)
  • 23 (not greater than 23)
  • 23.5 (greater than 23)

The value that makes the inequality \( 3r - 47.5 > 21.5 \) a true statement is 23.5.

Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?(1 point)
Responses

8
8

9
9

9.5
9.5

10

To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we'll first square both sides to eliminate the square root (while remembering that squaring both sides is valid since both sides are non-negative in this case):

  1. Square both sides: \[ 4x + 1 \leq (5.83)^2 \]

  2. Calculate \( (5.83)^2 \): \[ (5.83)^2 = 33.9889 \]

So the inequality becomes: \[ 4x + 1 \leq 33.9889 \]

  1. Subtract 1 from both sides: \[ 4x \leq 32.9889 \]

  2. Divide by 4: \[ x \leq \frac{32.9889}{4} \approx 8.247225 \]

Now we need to find which of the provided values for \( x \) satisfies the inequality \( x \leq 8.247225 \):

  • 8 (satisfies the inequality)
  • 9 (does not satisfy the inequality)
  • 9.5 (does not satisfy the inequality)
  • 10 (does not satisfy the inequality)

The value that makes the inequality \( \sqrt{4x + 1} \leq 5.83 \) true is 8.