What is the sum of all solutions to the equation |x + 3| = 4 ?

Question

A. -8
B. -6
C. 4
D. 8
E. 9

kunalcvrce · Answer

x+3=4 and x+3=-4

x=1,-7
sum =-6

B

akadiyan · Answer

X can have 2 values 1 and -7. The sum of which is equal to -6.

Ans: B

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JeffTargetTestPrep · Answer

Solving for x when (x + 3) is positive, we have:

x + 3 = 4

x = 1

Solving for x when (x + 3) is negative, we have:

-(x + 3) = 4

-x - 3 = 4

-x = 7

x = -7

The sum of the solutions is 1 + (-7) = -6.

Answer: B

BrushMyQuant · Answer

We need to find What is the sum of all solutions to the equation |x + 3| = 4 ?

We have two cases as we have |x + 3| 
 
   -   Case 1:  x+3 ≥ 0 or x ≥ -3
 
=> |x + 3| = x + 3
=> x + 3 = 4
=> x = 1

But the condition was x ≥ -3 and x = 1 ≥ -3
  => x = 1 is a  SOLUTION   
  -   Case 2:  x+3 ≤ 0 or x ≤ -3
 
 => |x + 3| = -(x + 3)
=> -(x + 3) = 4
=> -x - 3 = 4
=> x = -3 - 4 = -7

But the condition was x ≤ -3 and x = -7 ≤ -3
  => x = -7 is a  SOLUTION

=> Sum of all the solutions for x = 1 + -7 = -6

So,  Answer will be B 
Hope it helps!

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https://www.youtube.com/watch?v=huFiBk8PaGY

What is the sum of all solutions to the equation |x + 3| = 4 ?

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We have two cases as we have \|x + 3\|
-Case 1: x+3 ≥ 0 or x ≥ -3 => \|x + 3\| = x + 3 => x + 3 = 4 => x = 1 But the condition was x ≥ -3 and x = 1 ≥ -3 => x = 1 is a SOLUTION	-Case 2: x+3 ≤ 0 or x ≤ -3 => \|x + 3\| = -(x + 3) => -(x + 3) = 4 => -x - 3 = 4 => x = -3 - 4 = -7 But the condition was x ≤ -3 and x = -7 ≤ -3 => x = -7 is a SOLUTION

GMAT Problem Solving (PS) Questions

What is the sum of all solutions to the equation |x + 3| = 4 ?

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