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

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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]

Guest Aug 31, 2017

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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 $$(-2,∞)$$

gibsonj338  Aug 31, 2017
Sort:

#1
+1828
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

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