Question

Solve the inequality. (Lesson 5.7)

$\frac{1}{5}y\text{+14}\le \frac{13}{5}$

Short answer

The solution is $y\le -57$.

Step-by-step solution

Step-1 – Given

The given inequality is:$\frac{1}{5}y\text{+14}\le \frac{13}{5}$.

Step-2 – To determine

We have to solve the inequality$\frac{1}{5}y\text{+14}\le \frac{13}{5}$.

Step-3 – Calculation 

$\begin{array}{c}\frac{1}{5}y\text{+14}\le \frac{13}{5}\\ \frac{y+70}{5}\le \frac{13}{5}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{TakingLeastcommonfactor]}\\ y+70\le 13\\ y+70-70\le 13-70\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{Subtracting70onbothsides]}\\ y\le -57\end{array}$

Hence,$y\le -57$ is the required solution.