Answer
The solution is $\Big(-\dfrac{3}{2},\dfrac{13}{10}\Big)$
Work Step by Step
$\Big|5x+\dfrac{1}{2}\Big|-2\lt5$
Take $2$ to the right side of the inequality:
$\Big|5x+\dfrac{1}{2}\Big|\lt5+2$
$\Big|5x+\dfrac{1}{2}\Big|\lt7$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-7\lt5x+\dfrac{1}{2}\lt7$
$\textbf{Solve the inequality shown above:}$
$-7\lt5x+\dfrac{1}{2}\lt7$
Multiply the whole equation by $2$:
$2\Big(-7\lt5x+\dfrac{1}{2}\lt7\Big)$
$-14\lt10x+1\lt14$
Subtract $1$ from all three parts of the inequality:
$-14-1\lt10x+1-1\lt14-1$
$-15\lt10x\lt13$
Divide all three parts of the inequality by $10$:
$-\dfrac{15}{10}\lt\dfrac{10x}{10}\lt\dfrac{13}{10}$
$-\dfrac{3}{2}\lt x\lt\dfrac{13}{10}$
Expressing the solution in interval notation:
$\Big(-\dfrac{3}{2},\dfrac{13}{10}\Big)$
