Question

Solve 4(5x+7)≤13 . Write the solution in set builder notation.

example of set builder notation: {x|x>0}

Answer 1

Answer:

$\left\{x|x\leq-\dfrac{3}{4}\right\}$

Step-by-step explanation:

Given inequality:

$4(5x+7)\leq13$

Divide both sides by 4:

$\implies \dfrac{4(5x+7)}{4}\leq\dfrac{13}{4}$

$\implies 5x+7\leq \dfrac{13}{4}$

Subtract 7 from both sides:

$\implies 5x+7-7\leq \dfrac{13}{4}-7$

$\implies 5x\leq \dfrac{13}{4}-\dfrac{28}{4}$

$\implies 5x\leq -\dfrac{15}{4}$

Divide both sides by 5:

$\implies \dfrac{5x}{5}\leq \dfrac{-\frac{15}{4}}{5}$

$\implies \dfrac{5x}{5}\leq -\dfrac{15}{4}\times \dfrac{1}{5}$

$\implies x\leq -\dfrac{15}{20}$

$\implies x \leq -\dfrac{3}{4}$

Therefore, the solution in set builder notation is:

$\left\{x|x\leq-\dfrac{3}{4}\right\}$