Question

The work of a student trying to solve the equation 4(2x − 1) = 11 + 3x + 5 is shown below:Step 1: 4(2x − 1) = 11 + 3x + 5Step 2: 8x − 4 = 16 + 3xStep 3: 8x + 3x = 16 − 4Step 4: 11x = 24Step 5: x = 2.18In which step did the student first make an error and what is the correct step? Step 2: 8x − 1 = 16 + 3xStep 2: 8x − 8 = 6 + 3xStep 3: 8x − 3x = 16 + 4Step 3: 8x + 3x = 16 − 8

Answer 1

We have the equation
`4(2x-1)=11+3x+5`. Lets workout the solution ourselves to figure it out where the student made the first mistake:
Step 1:

`4(2x-1)=11+3x+5`

Step 2:

`8x-4=16+3x`

Step 3:

`8x-3x=16+4`

Step 4:

`5x=20`

Step 5:

`x=4`

We can conclude that the student made the first mistake in step 3. He added 3x to both sides of the equation instead of subtract 3x from both sides of the equation; he also subtracted 4 to both sides of the equation instead of add 4 pf both sides. The correct step is Step 3: 8x − 3x = 16 + 4