Question

Solve the absolute value Inequality. Express the answer using interval notation and graph the solution set.

$7|x+2|+5>4$

Short answer

The interval notation is $\left(-\infty ,\infty \right)$.

The graph of the solution is:

Step-by-step solution

Step 1. Determining the solution of Inequality.

Simplify the inequality as shown below:

$7|x+2|+5>4$

width="154" height="20" role="math">7|x+2|+5-5>4-5

$7|x+2|>-1$

$\frac{7|x+2|}{7}>-\frac{1}{7}$

$|x+2|>-\frac{1}{7}$

Step 2. Expressing the solution set in Interval Notation.

Now we know that the absolute value is always greater than 0.

It means for all x the given inequality satisfies the condition.

Hence, the required interval notation is $\left(-\infty ,\infty \right)$.

Step 3. Graphing the solution set.

The graph of the solution set is the set of all real numbers.

The required graph is shown below: