What is the solution to the compound inequality in interval notation? 4(x+1)>−4  or  2x−4≤−10

$4(x+1)>-4$ or $2x-4≤-10$

 

Firstly solve for x in the first inequality.

 

$4(x+1)>-4$

 

$4x+4>-4$

 

$4x-4+4>-4-4$

 

$4x-0>-4-4$

 

$4x>-4-4$

 

$4x>-8$

 

$\frac{4x}{4}>\frac{-8}{4}$

 

$\frac{1x}{1}>\frac{-8}{4}$

 

$1x>\frac{-8}{4}$

 

$x>\frac{-8}{4}$

 

$x>-\frac{8}{4}$

 

$x>-\frac{2}{1}$

 

$x>-2$

 

Secondly solve for x in the second inequality.

 

$2x-4≤-10$

 

$2x-4+4≤-10+4$

 

$2x-0≤-10+4$

 

$2x≤-10+4$

 

$2x≤-6$

 

$\frac{2x}{2}≤\frac{-6}{2}$

 

$\frac{1x}{1}≤\frac{-6}{2}$

 

$1x≤\frac{-6}{2}$

 

$x≤\frac{-6}{2}$

 

$x≤-\frac{6}{2}$

 

$x≤-\frac{3}{1}$

 

$x≤-3$

 

Thirdly put both answers together with the word "or" in between.

 

$x>-2$ or $x≤-3$

 

Forthly, put answer in interval notation.

 

$(-2,∞)$ or $(-∞,-3]$

 

$(-∞,-3]$ or $(-2,∞)$

 

Lastly, look at the list of A. B. C. and D. and figure out which one matches the answer.

 

A.  (-∞,-3] or $(-2,∞)$