Solving Multi-Step Inequalities

1
ObjectiveThe student will be able to
solve two-step equations using inverse operations
Designed by Skip Tyler, Varina High School
2
Two-step Equations
3
To solve two-step equations, undo the operations
by working backwards.

• Recall the order of operations as you answer
  these questions.
• Dividing by 2
• Subtracting 3

• Example
• Ask yourself,
• What is the first thing we are doing to x?
• What is the second thing?

To undo these steps, do the opposite operations
in opposite order.
4
Use a DO-UNDO chart as a shortcut to answering
the questions. In the table, write the opposite
operations in the opposite order

1. Draw the river
2. Add 3 to both sides
3. Simplify
4. Clear the fraction -Multiply both sides by 2
5. Simplify
6. Check your answer

• DO UNDO
• 2
• -3
• Follow the steps in the undo column to isolate
  the variable.

3 2
3 3
- 4 x -8 -4 3 -7
2 2
5
1) Solve 2x - 1 -3
2 - 1
1 2
1 1 2x -2 2
2 x -1 2(-1) - 1 -3 -2 1 -3

1. Draw the river
2. Add 1 to both sides
3. Simplify
4. Divide both sides by 2
5. Simplify
6. Check your answer

6
2) Solve
3 - 4
4 3
4 4 3 3 x
36 12 4 8

1. Draw the river
2. Add 4 to both sides
3. Simplify
4. Clear the fraction -Multiply both sides by 3
5. Simplify
6. Check your answer

7
3) Solve 3y 1 8

1. y 3
2. y -3
3. y
4. y

8
3) Solve
- 4 2
2 4

1. Draw the river
2. Clear the fraction - Multiply both sides by 2
3. Simplify
4. Add 4 to both sides
5. Simplify
6. Check your answer

d 4 6 4 4
d 10
9
4) Solve

1. d -7
2. d -19
3. d -17
4. d 17

10
5) Solve
-7 3
- 3 -7
Do/Undo Chart This one is tricky! Remember to
always use the sign in front of the number.
-3 -3
a 35

1. Draw the river
2. Subtract 3 from both sides
3. Simplify
4. Clear the fraction Multiply both sides by -7
5. Simplify
6. Check your answer

11
6) Solve 5z 16 51

1. z -35
2. z -7
3. z 35
4. z 7

12
7) Solve
3 5 1
- 1 5 3
- 1 - 1 5 5
3x 15 3 3 x 5

1. Draw the river
2. Subtract 1 from both sides
3. Simplify
4. Clear the fraction -Multiply both sides by 5
5. Simplify
6. Divide both sides by 3
7. Simplify
8. Check your answer