# How do you solve #abs(7 + 2x) = 9#?

##### 2 Answers

#### Explanation:

As The Absolute Value of the Expression is 9, we will have to solve the equation twice, once for positive and once for negative.

As.

So, Case 1 (Taking Positive):

Case 2 (Taking Negative) :

So,

Hope this helps.

#### Explanation:

#"the expression inside the absolute value bars can be"#

#"positive or negative so there are 2 possible solutions"#

#color(magenta)"Positive expression"#

#7+2x=9#

#"subtract 7 from both sides and divide by 2"#

#rArr2x=9-7=2rArrx=2/2=1#

#color(magenta)"Negative expression"#

#-(7+2x)=9#

#rArr-7-2x=9#

#"add 7 to both sides and divide by "-2#

#rArr-2x=9+7=16rArrx=16/(-2)=-8#

#color(blue)"As a check"# Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

#x=1to|7+2|=|9|=9#

#x=-8to|7-16|=|-9|=9#

#rArrx=-8" or "x=1" are the solutions"#