How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3? (4 points)
None
One
Two
Infinitely many
One
The work of a student trying to solve the equation 2(2x − 3) = 6 + 2x + 4 is shown below:
Step 1: 2(2x − 3) = 6 + 2x + 4
Step 2: 4x − 3 = 10 + 2x
Step 3: 4x − 2x = 10 + 3
Step 4: 2x = 13
Step 5: x = 6.5
In which step did the student first make an error and what is the correct step? (4 points)
Step 2: 4x − 6 = 10 + 2x
Step 2: 4x − 3 = 2 + 2x
Step 3: 4x + 2x = 10 + 3
Step 3: 4x − 2x = 10 - 3
The student made an error in Step 3. The correct step should be:
Step 3: 4x - 2x = 10 - 3