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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
8.8k points

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