Answer:
[tex]\left\{x|x\leq-\dfrac{3}{4}\right\}[/tex]
Step-by-step explanation:
Given inequality:
[tex]4(5x+7)\leq13[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4(5x+7)}{4}\leq\dfrac{13}{4}[/tex]
[tex]\implies 5x+7\leq \dfrac{13}{4}[/tex]
Subtract 7 from both sides:
[tex]\implies 5x+7-7\leq \dfrac{13}{4}-7[/tex]
[tex]\implies 5x\leq \dfrac{13}{4}-\dfrac{28}{4}[/tex]
[tex]\implies 5x\leq -\dfrac{15}{4}[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{5x}{5}\leq \dfrac{-\frac{15}{4}}{5}[/tex]
[tex]\implies \dfrac{5x}{5}\leq -\dfrac{15}{4}\times \dfrac{1}{5}[/tex]
[tex]\implies x\leq -\dfrac{15}{20}[/tex]
[tex]\implies x \leq -\dfrac{3}{4}[/tex]
Therefore, the solution in set builder notation is:
[tex]\left\{x|x\leq-\dfrac{3}{4}\right\}[/tex]
