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

A. (−∞, −3] or (−2, ∞)

B. (−∞, −3] or (2, ∞)

C. (−∞, −2) or [3, ∞)

D. (−3, −2]

Guest Aug 31, 2017

#1**0 **

\(4(x+1)>-4\) 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 \((-2,∞)\)

.gibsonj338 Aug 31, 2017

#1**0 **

Best Answer

\(4(x+1)>-4\) 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 \((-2,∞)\)

gibsonj338 Aug 31, 2017