Question
Solve the absolute value equation.
|2x + 6| = 2
|2x + 6| = 2
Answers
GPT 3.5
To solve the absolute value equation, we can break it down into two separate equations:
1. 2x + 6 = 2
Subtract 6 from both sides:
2x = 2 - 6
2x = -4
Divide both sides by 2:
x = -2
2. -(2x + 6) = 2
Distribute the negative sign:
-2x - 6 = 2
Add 6 to both sides:
-2x = 2 + 6
-2x = 8
Divide both sides by -2 (remember to flip the inequality sign since we are dividing by a negative number):
x = 8 / -2
x = -4
The solutions to the absolute value equation are x = -2 and x = -4.
1. 2x + 6 = 2
Subtract 6 from both sides:
2x = 2 - 6
2x = -4
Divide both sides by 2:
x = -2
2. -(2x + 6) = 2
Distribute the negative sign:
-2x - 6 = 2
Add 6 to both sides:
-2x = 2 + 6
-2x = 8
Divide both sides by -2 (remember to flip the inequality sign since we are dividing by a negative number):
x = 8 / -2
x = -4
The solutions to the absolute value equation are x = -2 and x = -4.