78.9k views
3 votes
Solve the inequality. Write your answer in Interval Notation. Show your work.

4 ( x + 2 ) - 5x < x + 20

User Athafoud
by
8.2k points

2 Answers

3 votes

Answer:

(-6, +∞)

Explanation:

4(x + 2) - 5x < x + 20 Distribute the 4

4x + 8 - 5x < x + 20 combine like terms

-x + 8 < x + 20 Add x to both sides

-x + x + 8 < x + x + 20

8< 2x + 20 Subtract 20 from both sides

-12 < 2x Divide both sides by 2


(-12)/(2) <
(2x)/(2)

-6 < x

x > -6

My solutions are all the numbers larger than -6.

Helping in the name of Jesus.

User Kayze
by
7.4k points
3 votes

Answer:

x > -6

Detailed explanation:

Hi there! Our task is to solve the inequality.

First, use the distributive property:


\mathbf{4(x+2)-5x < x+20}

Combine like terms:


\mathbf{4x+8-5x < x+20}


\mathbf{-x+8 < x+20}

Subtract x from each side:


\mathbf{-x-x+8 < 20}

Combine like terms:


\mathbf{-2x+8 < 20}

Subtract 8 from each side:


\mathbf{-2x < 20-8}


\mathbf{-2x < 12}

Reverse the inequality sign:


\mathbf{x > -6}


\bigstar Therefore, x > -6.

User Pdwalker
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories