Question

checking solutions tell whether the given value is a solution of the inequality. 29. $4k < k + 8; k = 3$ 30. $\frac{w}{3} geq w - 12; w = 15$ 31. $7 - 2y > 3y + 13; y = -1$ 32. $\frac{3}{4}b - 2 leq 2b + 8; b = -4$

Explanation:

Step1: Substitute k=3 into inequality 29

$4(3) < 3 + 8$

Step2: Simplify both sides (29)

$12 < 11$

Step3: Substitute w=15 into inequality 30

$\frac{15}{3} \geq 15 - 12$

Step4: Simplify both sides (30)

$5 \geq 3$

Step5: Substitute y=-1 into inequality 31

$7 - 2(-1) > 3(-1) + 13$

Step6: Simplify both sides (31)

$9 > 10$

Step7: Substitute b=-4 into inequality 32

$\frac{3}{4}(-4) - 2 \leq 2(-4) + 8$

Step8: Simplify both sides (32)

$-5 \leq 0$

Answer:

1. $12 < 11$ is false, so $k=3$ is not a solution.
2. $5 \geq 3$ is true, so $w=15$ is a solution.
3. $9 > 10$ is false, so $y=-1$ is not a solution.
4. $-5 \leq 0$ is true, so $b=-4$ is a solution.