Common Errors in Solving Equations

Find the error in the problem below
19 - 2k = 3k - 1
     +3k   +3k
19 + 1k = -1
-19           -19
k = -20

• They should have divided by 1 for the last step
• They should add 19 instead of subtracting 19
• I can not find an error
• Instead of adding 3k they should subtract 3k

Find the Error
What error did the student make when solving the equation:
1/5x + 6 = 3/5x + 5
1x + 6 = 3x + 5
-2x + 6 = 5
-2x = -1
x = 1/2

• The student found an incorrect common denominator
• The student did not multiply all terms by the common denominator
• The student did not use opposite operations appropriately
• The student did not correctly eliminate the variable from one side of the equation

How many solutions does the equation below have?
5 + 2(n + 1) = 2n

• Identity
• One Solution
• No Solution
• Two Solutions

How many solutions does the equation below have?
5h - 7 = 5(h - 2) + 3

• Identity
• No solution
• Three Solutions
• One Solution

How many solutions does the equation below have?
6(3a +1) - 30 = 3(2a - 4)

• Identity
• No Solution
• Three Solutions
• One Solution

How many solutions does the equation below have?
6(3a +1) - 30 = 3(2a - 4)

• Identity
• No Solution
• Three Solutions
• One Solution

Is the solution below correct?
5d = 2d - 18
-2d   -2d
3d = -18
d = 6

• Yes
• No

Is the solution below correct?
-6z + 13 = 7z
+6z           +6z
13 = 13z
z = 1

• Yes
• No

Solve
6.78x - 5.2 = 4.33x + 2.15

• 0.66
• -0.27
• -1.24
• 3

Where was the mistake made?

5d = 2d - 18

-2d -2d

3d = -18

d = 6

• Subtracted 2d instead of adding

• Should have gotten -6 when dividing -18 by 3

• Should have added 18 to both sides first

• Should have subtracted 5d from both sides first