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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]

 Aug 31, 2017

Best Answer 

 #1
avatar+1904 
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\(4(x+1)>-4\) 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 \((-2,∞)\)

.
 Aug 31, 2017
 #1
avatar+1904 
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

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