Question

1. solve the inequality. then, choose the graph for the solution.

53 ≤ 3z + 29 - 11z
z ≥ -3
z ≥ 12/7
z ≤ 3
z ≤ -3

Explanation:

Step1: Combine like - terms

Combine the $z$ terms on the right - hand side of the inequality $53\leq3z + 29-11z$.
$53\leq(3z-11z)+29$, so $53\leq - 8z+29$.

Step2: Isolate the term with $z$

Subtract 29 from both sides of the inequality:
$53 - 29\leq-8z+29 - 29$, which gives $24\leq - 8z$.

Step3: Solve for $z$

Divide both sides of the inequality by - 8. Remember that when dividing an inequality by a negative number, the direction of the inequality sign changes.
$\frac{24}{-8}\geq\frac{-8z}{-8}$, so $z\leq - 3$.

Answer:

$z\leq - 3$ (corresponding to the graph where the arrow points to the left and the closed - circle is at $-3$)