To solve this equation, we need to consider two cases: when the expression inside the absolute value bars is positive and when it is negative.
Case 1: When 2x - 1 >= 0 This means that 2x - 1 is positive, so the absolute value bars can be removed. Therefore, the equation becomes: 2x - 1 + 7 = 8 2x + 6 = 8 2x = 2 x = 1
Case 2: When 2x - 1 < 0 This means that 2x - 1 is negative, so it becomes -(2x - 1) when the bars are removed. Therefore, the equation becomes: -(2x - 1) + 7 = 8 -2x + 1 + 7 = 8 -2x + 8 = 8 -2x = 0 x = 0
So the solution to the equation is x = 1 or x = 0.
To solve this equation, we need to consider two cases: when the expression inside the absolute value bars is positive and when it is negative.
Case 1: When 2x - 1 >= 0
This means that 2x - 1 is positive, so the absolute value bars can be removed.
Therefore, the equation becomes:
2x - 1 + 7 = 8
2x + 6 = 8
2x = 2
x = 1
Case 2: When 2x - 1 < 0
This means that 2x - 1 is negative, so it becomes -(2x - 1) when the bars are removed.
Therefore, the equation becomes:
-(2x - 1) + 7 = 8
-2x + 1 + 7 = 8
-2x + 8 = 8
-2x = 0
x = 0
So the solution to the equation is x = 1 or x = 0.