Step 1: |x − 5| + 2 = 5
Step 2: |x − 5| = 5 − 2
Step 3: |x − 5| = 3
Which of the following is a correct next step to solve the equation? (1 point)
x + 5 = −3
−x − 5 = 3
x − 5 = −3
x + 5 = 3
if
|x − 5| = 3
then
(x-5) = 3
or
-(x-5) = 3 which is x-5 = -3 ......the third one down
which is the only choice that still uses "x-5" ?
To solve the equation |x − 5| = 3, you can think of it as two separate equations:
1. x - 5 = 3
2. x - 5 = -3
The absolute value equation can have two possible solutions because absolute value measures the distance from 0, so both the positive and negative versions of the equation need to be considered.
Therefore, the correct next step to solve the equation is to consider both possibilities:
1. x - 5 = 3
Adding 5 to both sides of the equation, we get:
x = 8
2. x - 5 = -3
Adding 5 to both sides of the equation, we get:
x = 2
So, the two possible solutions for the equation |x − 5| = 3 are x = 8 and x = 2.
None of the options provided match the correct next step for solving the equation.