1. Solving One-Step Equations
Lesson 4
Linear Equations
Solving One-Step Equations

2. Warm-Up
Evaluate each expression for x = −4.
x + 7
3x − 1 −x x2

3. Solving One-Step Equations
Target:
Use inverse operations to solve one-step equations.

4. The Properties of Equality
For any numbers a, b and c:
If a = b then a + c = b + c (Addition Property of Equality)
If a = b then a – c = b – c (Subtraction Property of Equality)
If a = b then a ∙ c = b ∙ c (Multiplication Property of Equality)
If a = b then a ÷ c = b ÷ c (Division Property of Equality)

5. Vocabulary
Zero Pair: One positive integer chip paired with one negative integer chip.
Inverse Operation: Operations that undo each other.

8. Example 1ab Solve for x. Check your solution. x – 6 = 22 + 6 + 6
x = 28
28 – 6 = 22
8x = 88
x = 11
8(11) = 88

9. Example 1cd Solve for x. Check your solution. x + 10 = – 7 – 10 – 10
– – 10
x = – 17
(– 17) + 10 = – 7

10. Example 2a
Write an equation for the statement. Solve the equation and check your solution. The product of eleven and a number is seventy-seven. 11x = x = 7 11(7) = 77

11. Example 2b
Write an equation for the statement. Solve the equation and check your solution. The sum of a number and 52 is 98. x + 52 = 98 – 52 – 52 x = = 98

12. Example 2c
Write an equation for the statement. Solve the equation and check your solution. A number decreased by 13 is 214. x – 13 = x = – 13 = 214

13. Example 3
The sum of Kirk’s age and his dad’s age is 53. Kirk is 14. Write an equation that represents this situation using d to represent the dad’s age. Solve the equation and check your solution d = 53 – 14 – 14 d = = 53 Kirk’s dad is 39 years old.

14. Exit Problems
Solve each equation for x.
x – 70 = 138
11x = 66

15. Communication Prompt
How are manipulatives helpful when solving one-step
equations?