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

Question

Hazel Anglin · Accepted Answer

#x = 1, -8#.

Since the expression's absolute value is nine, we must solve the equation twice—once for the positive and once for the negative. As. #|a| = a = |-a|#. Thus, Case 1 (Looking Forward): #color(white)(xxx)(7 + 2x) = 9# #rArr cancel7 + 2x cancel(- 7) = 9 - 7# [Subtract #7# from both sides] #rArr 2x = 2# #rArr (2x)/2 = 2/2# [Dividing both sides by #2#] #rArr x = 1# Example 2 (Assuming Negative): #color(white)(xxx)-(7 + 2x) = 9# #rArr - 7 - 2x = 9# [Distributive Property] #rArr cancel(-7) - 2x + cancel7 = 9 + 7# [Add #7# to both sides] #rArr -2x = 16# #rArr (-2x)/-2 = 16/-2# [Dividing both sides by #-2#] #rArr x = -8# So, #x# has two values, #1, -8#. I hope this is useful.

Eva Abramson · Answer

#x=-8" or "x=1#

#"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"#

Ethan Adkins · Answer

undefined To solve the equation $|7 + 2x| = 9$, we first isolate the absolute value expression.

1. Set up two equations:
   $7 + 2x = 9$ and $7 + 2x = -9$.
   
2. Solve each equation separately:
   For $7 + 2x = 9$:
   $$2x = 9 - 7$$
   $$2x = 2$$
   $$x = 1$$
   
   For $7 + 2x = -9$:
   $$2x = -9 - 7$$
   $$2x = -16$$
   $$x = -8$$
   
3. So, the solutions are $x = 1$ and $x = -8$.