Question

Daniel worked out the problem below:4x + 12x + 8 = 2

Which step first shows his mistake?

Step 1: 4x + 12x + 8 = 2
Step 2: 48x + 8 = 2
Step 3: 48x + 8 - 8 = 2 - 8
Step 4: 48x = -6
Step 5: x = -8

Answer 1

The mistake occurred in Step 2 of Daniel's algebra problem, where he incorrectly combined like terms, which should have resulted in 16x instead of 48x.

Step-by-step explanation:

The mistake Daniel made in his algebra problem is in Step 2 where he combined like terms incorrectly. The correct method to combine 4x and 12x is to add the coefficients to get 16x, not 48x as Daniel did. His mistake altered subsequent steps and led to the wrong value for x.

Correct Solution:

Combine like terms: 4x + 12x + 8 = 16x + 8

Subtract 8 from both sides: 16x + 8 - 8 = 2 - 8

Simplify both sides: 16x = -6

Divide both sides by 16: x = -6/16

Simplify the fraction: x = -3/8

Therefore, the correct solution should give x = -3/8, not x = -8 as Daniel concluded.