Question

23 for which compound inequalities is 5 in the solution set? 5 is a solution 5 is not a solution 12 ≤ 4x - 5 ≤ 27 -6 ≤ 3x < 17 7 ≥ 5x - 21 > 0 3 < 3x - 15 < 32 -2 ≤ x + 12 < 15 2 < -x + 10 < 8

Explanation:

Step1: Test $12 \leq 4x - 5 \leq 27$

Substitute $x=5$:
$12 \leq 4(5)-5 \leq 27 \implies 12 \leq 15 \leq 27$
This is true.

Step2: Test $-6 \leq 3x < 17$

Substitute $x=5$:
$-6 \leq 3(5) < 17 \implies -6 \leq 15 < 17$
This is true.

Step3: Test $7 \geq 5x - 21 > 0$

Substitute $x=5$:
$7 \geq 5(5)-21 > 0 \implies 7 \geq 4 > 0$
This is true.

Step4: Test $3 < 3x - 15 < 32$

Substitute $x=5$:
$3 < 3(5)-15 < 32 \implies 3 < 0 < 32$
This is false.

Step5: Test $-2 \leq x + 12 < 15$

Substitute $x=5$:
$-2 \leq 5+12 < 15 \implies -2 \leq 17 < 15$
This is false.

Step6: Test $2 < -x + 10 < 8$

Substitute $x=5$:
$2 < -5+10 < 8 \implies 2 < 5 < 8$
This is true.

Answer:

5 is a solution:

$12 \leq 4x - 5 \leq 27$, $-6 \leq 3x < 17$, $7 \geq 5x - 21 > 0$, $2 < -x + 10 < 8$

5 is not a solution:

$3 < 3x - 15 < 32$, $-2 \leq x + 12 < 15$