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
what are the solutions of inequality 1? 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: Divide both sides by 4

To isolate the term with \( z \), divide both sides of the inequality \( 4(1.7z + 1.75) < 34.2 \) by 4.
\( \frac{4(1.7z + 1.75)}{4} < \frac{34.2}{4} \)
Simplifying, we get \( 1.7z + 1.75 < 8.55 \).

Step2: Subtract 1.75 from both sides

Subtract 1.75 from both sides to isolate the term with \( z \):
\( 1.7z + 1.75 - 1.75 < 8.55 - 1.75 \)
Simplifying, we get \( 1.7z < 6.8 \).

Step3: Divide both sides by 1.7

Divide both sides by 1.7 to solve for \( z \):
\( \frac{1.7z}{1.7} < \frac{6.8}{1.7} \)
Simplifying, we find \( z < 4 \).

Answer:

B. \( z < 4 \)