Question

Solve, write your answer in interval notation and graph the solution set.

14a. |5y-2| less than 13

14b. |x+1| greater than or equal to 5

Answer 1

Solve, write your answer in interval notation and graph the solution set.

14a. $|5y - 2| < 13$

14b. $|x + 1| \geq 5$

**Solution:**

14a $|5y - 2| < 13$

$$\begin{array}{l} -13 < 5y - 2 < 13 \\ -13 + 2 < 5y < 13 + 2 \\ -11 < 5y < 15 \\ -\frac{11}{5} < y < 3 \\ y \in (-0.22, 3) \\ \end{array}$$ $$\xrightarrow[ -0.22]{+} \begin{array}{c} \text{0} \\ 3 \end{array} \xrightarrow{\text{y}}$$

**Answer:** $y \in (-0.22, 3)$

14b. $|x + 1| \geq 5$

$$\begin{array}{l} \left[ \begin{array}{l} x + 1 \geq 5 \\ x + 1 \leq -5 \end{array} \right. \\ \left[ \begin{array}{l} x \geq 4 \\ x \leq -6 \end{array} \right. \\ x \in (-\infty, -6] \cup [4, +\infty) \\ \end{array}$$ $$\xrightarrow[ -6]{+} \begin{array}{c} \text{0} \\ 4 \end{array} \xrightarrow{\text{y}}$$

**Answer:** $x \in (-\infty, -6] \cup [4, +\infty)$