A student solves the following problem: 2(x - 2) + 5x = 24
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
The student made a mistake in step 3. They added 4 to both sides of the equation, which is incorrect. The correct operation should be to add 4 to both sides of the equation to get:
10x - 4 + 4 = 24 + 4
This simplifies to:
10x = 28
By adding 4 to both sides, the student made an error in their calculations.
The mistake the student made is in Step 3. They added 4 to only the right side of the equation, but they failed to add 4 to both sides of the equation. This is an error in maintaining the equivalence of the equation. Here's the corrected version:
Step 3: 10x - 4 + 4 = 24 + 4
By adding 4 to both sides of the equation, the equation should be:
10x - 4 + 4 = 24 + 4
10x = 28
Therefore, the correct equation is 10x = 28 in Step 4, leading to the correct solution of x = 2.8 in Step 5 and Step 6.