Question

Solve the inequality.

$\frac{2}{3}x+9\le \frac{17}{2}$

Short answer

The solution is$x\le -\frac{3}{4}$ .

Step-by-step solution

Step-1 – Given

The given inequality is:$\frac{2}{3}x+9\le \frac{17}{2}$.

Step-2 – To determine

We have to solve the inequality$\frac{2}{3}x+9\le \frac{17}{2}$

Step-3 – Calculation 

Solve the given inequality.

$\begin{array}{c}\frac{2}{3}x+9\le \frac{17}{2}\\ \frac{2x+27}{3}\le \frac{17}{2}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{TakingLeastcommonfactor]}\\ \left(2x+27\right)·2\le 17·3\\ \left(2x+27\right)·2\le 51\\ 4x+54\le 51\\ 4x+54-54\le 51-54\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{Subtracting54onbothsides]}\\ 4x\le -3\\ \frac{4x}{4}\le -\frac{3}{4}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{Dividing4onbothsides]}\\ x\le -\frac{3}{4}\end{array}$

Hence, $x\le -\frac{3}{4}$is the required solution.