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

Brittney Lord

Brittney Lord

Answered question

2021-05-31

Solve each inequality. |2x+7|13

Answer & Explanation

AGRFTr

AGRFTr

Skilled2021-06-01Added 95 answers

Step 1
The given inequality is:
|2x+7|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+713and2x+713
Step 2
Solving for first inequality, we get:
2x+713
2x+77137
2x6
2x(12)6(12)
x3
x3
The second inequality condition becomes:
2x+713
2x+77137
2x+77137
2x20
2x(12)20(12)
x10
x10
Hence, the solution set in interval notation is:
[-3,10]

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