`10(x+1) = 1/2(x - 18)` Solve the equation. Check the solution.

Textbook Question

Chapter 3, 3.1 - Problem 71 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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nees101's profile pic

nees101 | Student, Graduate | (Level 2) Adjunct Educator

Posted on

10(x+1)=`1/2` (x-18)

20(x+1)=x-18

20x+20=x-18

20x-x=-18-20

19x=-38

x=`-38/19` =-2

Therefore x=-2

mangoes123's profile pic

mangoes123 | Student | (Level 1) eNoter

Posted on

First, multiply both sides by two to get rid of the 1/2 

you're left with:

`20(x+1)=x-18`

Then, distribute the 20 in front of (x+1) and you're left with:

`20x+20=x-18`

then, combine like terms by subtracting 20 from -18 and (1)x from 20x

`19x=-38`

Divide both sides by 19 to get x by itself:

`x=-2`

check:

plug -2 in for x 

`20(-2+1)=1/2(-2-18)`

solve:

`10(-1)=1/2(-20)`

`-10=-10`

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

The first step is to distribute the numbers outside of the parentheses to those inside:

`10(x + 1) = 1/2 (x - 18)`

`10x + 10 = 1/2x - 9`

now move like terms to the same side by adding or subtracting numbers:

`10x - 1/2 x + 10 - 10 = 1/2x - 1/2x - 9 -10`

`10x - 1/2x = -9 - 10`

combine:

9.5 x = -19

now we have to get x alone and 9.5 is in the way and since it is being multiplied by 9.5 we must do the opposite and divide:

`(9.5x)/ 9.5 = -19/9.5`

x = -2

to check:

`10(-2 + 1) = 1/2 (-2 - 18)`

`10 (-1) = 1/2 (-20)`

-10 = -10

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