Question

The table shows the solution to the equation |2x − 5| − 2 = 3:

Step 1
|2x − 5| = 3 + 2


Step 2
|2x − 5| = 5

Which is the first incorrect step?

Step 3
2x − 5 = 5 or 2x − 5 = −5

Step 4
2x = 10 or 2x = 0

Step 5
x = 5 or x = 0

Answer 1

|2x - 5| - 2 = 3 |add 2 to both sides

|2x - 5| = 5

2x - 5 = 5 or 2x - 5 = -5 |add 5 to both sides

2x = 10 or 2x = 0 |divide both sides by 2

x = 5 or x = 0

All steps are correct.

Answer 2

All steps are correct

Explanation:

|2x − 5| − 2 = 3

Step 1

|2x − 5| = 3 + 2 (adding 2 on both sides)

Step 2

|2x − 5| = 5

Step 3

2x − 5 = 5 or 2x − 5 = −5 (on opening the modulus, we get 2 cases)

Step 4

2x = 10 or 2x = 0 (adding 5 on both sides)

Step 5

x = 5 or x = 0 (dividing by 2 on both sides)

Hence, each step was correct