Question

solve the following inequalities and graph your solution. ≤ ≥

1. 2(t + 2) + 3t ≤ -2(t - 4) + 10.
2. find the solution set for the inequality using the given replacement set. {7, 8, 9, 10, 11}.

5n - 18 ≥ 32

Explanation:

Problem 4

Step1: Expand both sides

$2t + 4 + 3t \leq -2t + 8 + 10$

Step2: Combine like terms

$5t + 4 \leq -2t + 18$

Step3: Add $2t$ to both sides

$5t + 2t + 4 \leq 18$
$7t + 4 \leq 18$

Step4: Subtract 4 from both sides

$7t \leq 18 - 4$
$7t \leq 14$

Step5: Divide by 7

$t \leq \frac{14}{7}$
$t \leq 2$

Step6: Graph the solution

On the number line, plot a closed dot at 2, then draw an arrow pointing left (towards negative infinity) to represent all values less than or equal to 2.

Step1: Solve the inequality first

$5n - 18 \geq 32$
$5n \geq 32 + 18$
$5n \geq 50$
$n \geq 10$

Step2: Match with replacement set

From $\{7, 8, 9, 10, 11\}$, select values $\geq 10$.

Answer:

$t \leq 2$
(Graph: Closed dot at 2, arrow left along the number line)

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Problem 5