Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation.
-$\left|\frac{1}{2} x+\frac{1}{5}\right|+\frac{1}{4}=\frac{7}{4}$

A) $\left(-\infty,-\frac{17}{5}\right] \cup\left[\frac{13}{5}, \infty\right)$

B) $\left\{-\frac{17}{5}, \frac{13}{5}\right\}$

C) $\left\{\frac{13}{5}\right\}$

D) $\left\{0, \frac{13}{5}\right\}$

Question

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation.
-$\left|\frac{1}{2} x+\frac{1}{5}\right|+\frac{1}{4}=\frac{7}{4}$

A) $\left(-\infty,-\frac{17}{5}\right] \cup\left[\frac{13}{5}, \infty\right)$

B) $\left\{-\frac{17}{5}, \frac{13}{5}\right\}$

C) $\left\{\frac{13}{5}\right\}$

D) $\left\{0, \frac{13}{5}\right\}$

Quizplus · Accepted Answer

First, isolate the absolute value expression: $\left|\frac{1}{2} x+\frac{1}{5}\right| = \frac{7}{4} - \frac{1}{4} = \frac{3}{2}$. Then, solve the equation $\frac{1}{2} x+\frac{1}{5} = \frac{3}{2}$ and $\frac{1}{2} x+\frac{1}{5} = -\frac{3}{2}$. Solving these gives $x = \frac{13}{5}$ and $x = -\frac{17}{5}$, respectively.

Solve the Given Equation or Inequality ∣12x+15∣+14=74\left|\frac{1}{2} x+\frac{1}{5}\right|+\frac{1}{4}=\frac{7}{4}​21​x+51​​+41​=47​ A) (−∞,−175]∪[135,∞)\left(-\infty,-\frac{17}{5}\right] \cup\left[\frac{13}{5}, \infty\right)(−∞,−517​]∪[513​,∞)

Solve the Given Equation or Inequality $\left|\frac{1}{2} x+\frac{1}{5}\right|+\frac{1}{4}=\frac{7}{4}$ A) $\left(-\infty,-\frac{17}{5}\right] \cup\left[\frac{13}{5}, \infty\right)$