Question

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

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asked 2021-05-31
Solve each inequality. \(|2x+7|\leq 13\)

Answers (1)

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]
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