Question

What is the graph of the solution to the following compound inequality? –6x – 1 < –25 or 3x + 4 ≤ –5

Answer 1

Answer:

$x>4$ or $x \leq -3$

Step-by-step explanation:

Given :$-6x -1 < -25$ or$3x + 4 \leq -5$

Solving first inequality :

$-6x-1$

Add 1 to both sides

$\Rightarrow -6x-1+1$

Divide both sides by 6

$\Rightarrow \frac{6}{6}x>\frac{24}{6}\\\Rightarrow x>4$

Solving second inequality:

$3x + 4 \leq -5$

Subtract 4 from both sides

$\Rightarrow 3x+4-4 \leq -5-4\\\Rightarrow 3x \leq -9$

Divide both sides by 3

$\Rightarrow \frac{3}{3}x \leq \frac{-9}{3}$

$\Rightarrow x \leq -3$

So, $x>4$ or $x \leq -3$

Refer the attached graph