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]

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]