Question

solve the following inequalities and graph your solution.

1. $3m - 9(m + 2) \le - (2m + 10)$.

1. find the solution set for the inequality using the given replacement set.

$4n - 11 \ge 25$ ${7, 8, 9, 10, 11}$.

Explanation:

Step1: Expand both sides of inequality

$3m - 9m - 18 \leq -2m - 10$

Step2: Combine like terms

$-6m - 18 \leq -2m - 10$

Step3: Isolate m terms to left

$-6m + 2m \leq -10 + 18$

Step4: Simplify both sides

$-4m \leq 8$

Step5: Divide by -4, reverse inequality

$m \geq -2$
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Step1: Test n=7 in the inequality

$4(7)-11=28-11=17$, $17
ot\geq 25$

Step2: Test n=8 in the inequality

$4(8)-11=32-11=21$, $21
ot\geq 25$

Step3: Test n=9 in the inequality

$4(9)-11=36-11=25$, $25 \geq 25$

Step4: Test n=10 in the inequality

$4(10)-11=40-11=29$, $29 \geq 25$

Step5: Test n=11 in the inequality

$4(11)-11=44-11=33$, $33 \geq 25$

Answer:

1. For $3m - 9(m + 2) \leq -(2m + 10)$:

Solution: $m \geq -2$
(Graph: Closed dot at $-2$ on the number line, arrow pointing to the right)

1. For $4n - 11 \geq 25$ with replacement set $\{7, 8, 9, 10, 11\}$:

Solution set: $\{9, 10, 11\}$