1. Foundations of Algebra
Solving
Two-Step Equations
Foundations of Algebra

2. What is a Two-Step Equation?
An equation written in the form
Ax + B = C , where two different algebraic operations are being performed on the variable.

3. Examples of Two-Step Equations
y/4 + 3 = 12
5n + 4 = 6
n/2 – 6 = 4

4. Steps for Solving Two-Step Equations
Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation.
Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.
Steps for Solving Two-Step Equations

5. Opposite Operations
Addition 
Subtraction
Multiplication 
Division

6. Helpful Hints?
Identify what operations are on the variable side. (Add, Sub, Mult, Div)
“Undo” the operation by using opposite operations.
Whatever you do to one side, you must do to the other side to keep equation balanced.

7. To solve two-step equations, undo the operations by working backwards.
Recall the order of operations as you answer these questions. 1)
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.

8. Solve the equations by doing the opposite operations in the opposite order.
Add 3 to both sides
Simplify
Clear the fraction -Multiply both sides by 2
Check your answer

9. 2) Solve 2x - 1 = -3 Add 1 to both sides Simplify
Divide both sides by 2
Check your answer

10. 3) Solve Add 4 to both sides Simplify
Clear the fraction -Multiply both sides by 3
Check your answer

11. 4) Solve 3y – 1 = 8
y = 3
y = -3
y =

12. 5) Solve Clear the fraction - Multiply both sides by 2 Simplify
Add 4 to both sides
Check your answer

13. 6) Solve
d = -7
d = -19
d = -17
d = 17

14. 7) Solve Subtract 3 from both sides Simplify
Clear the fraction – Multiply both sides by -7
Check your answer
This one is tricky! Remember to always use the sign in front of the number.

15. 8) Solve 5z + 16 = 51
z = -35
z = -7
z = 35
z = 7

16. 9) Solve Subtract 1 from both sides Simplify
Clear the fraction - Multiply both sides by 5
Divide both sides by 3
Check your answer

17. 2x – 5 = 17
3y + 7 = 25
5n – 2 = 38
12b + 4 = 28
Try These Examples

18. x = 11
y = 6
n = 8
b = 2
Check your answers!!!