Question

# Solve each inequality. |2x+7|\leq 13

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Solve each inequality. $$|2x+7|\leq 13$$

2021-06-01
Step 1
The given inequality is:
$$|2x+7|\leq 13$$
To solve the given inequality involving absolute values:
First, finding the value inside the absolute value, sign must be less than or equal to 13 units away from zero.
Thus, the inequality is equivalent to the following:
$$-2x+7\leq 13 and -2x+7 \geq 13$$
Step 2
Solving for first inequality, we get:
$$-2x+7\leq 13$$
$$-2x+7-7\leq 13-7$$
$$-2x\leq 6$$
$$-2x(\frac{1}{2})\leq 6(\frac{1}{2})$$
$$-x\leq 3$$
$$x\geq -3$$
The second inequality condition becomes:
$$-2x+7\geq -13$$
$$-2x+7-7\geq -13-7$$
$$-2x+7-7\geq -13-7$$
$$-2x\geq -20$$
$$-2x(\frac{1}{2})\geq -20(\frac{1}{2})$$
$$-x\geq -10$$
$$x\leq 10$$
Hence, the solution set in interval notation is:
[-3,10]