+0

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

0
198
1

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
+1794
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
Sort:

#1
+1794
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

### 13 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details