Question

5.7 ps 14
challenge solve each of the given inequalities for z. which of the inequalities have -5 as a solution?
inequality 1: 4(1.7z + 1.75) < 34.2
inequality 2: 2(2.6z + 2.5) ≥ -10.6

a. z ≥

b. z < 4

c. z >

d. z ≤

what are the solutions of inequality 2? select the correct choice below and fill in the answer box to complete your choice.

a. z ≤

b. z <

c. z ≥

d. z >

Explanation:

Step1: Solve Inequality 2

Start with \( 2(2.6z + 2.5) \geq -10.6 \). Divide both sides by 2: \( 2.6z + 2.5 \geq \frac{-10.6}{2} \)
\( 2.6z + 2.5 \geq -5.3 \)

Step2: Isolate z term

Subtract 2.5 from both sides: \( 2.6z \geq -5.3 - 2.5 \)
\( 2.6z \geq -7.8 \)

Step3: Solve for z

Divide both sides by 2.6: \( z \geq \frac{-7.8}{2.6} \)
\( z \geq -3 \)

Answer:

C. \( z \geq -3 \)