Question

A student solves the following problem:

Problem: 2(x−3)+3x=19
Step 1: 2x−6+3x=19
Step 2: 6x−6=19
Step 3: 6x−6 + 6=19 + 6
Step 4: 6x=25
Step 5: 6x6=256
Step 6: x≈4.17
Where is the mistake? What did the student do incorrectly?

Responses

Step 3: Student should have subtracted 6 from both sides, not added 6.

Step 5: Student should have subtracted 6 from both sides, not divided by 6

Step 1: Student should have only distributed the 2 to the x and not the x & 3.

Step 2: Student should have added 2x + 3x = 5x, not 2 x 3 = 6x

Answer 1

error in Step 2

Explanation:

2(x - 3) + 3x = 19

Step 1 : 2x - 6 + 3x = 19 ← simplify left side by collecting like terms

Step 2 : 5x - 6 = 19 ← add 6 to both sides

Step 3 : 5x - 6 + 6 = 19 + 6

Step 4 : 5x = 25 ← divide both sides by 5

Step 5 : x = 5

Error was made by student in Step 2 who should have added 2x and 3x, not multiplied 2 × 3