This document provides instructions for solving two-step equations involving fractions and decimals. It outlines the key rules: 1) keep the equation balanced, 2) simplify each side by combining like terms, 3) move the variable to one side using inverse operations, and 4) use inverse operations. It then works through several examples of solving two-step equations with fractions and decimals, applying the outlined rules. The objective is to isolate the variable to find its value.

1. OBJECTIVE: How do we solve
two-step equations involving fractions
and decimals?
Do Now
Solve the following equations.
1.) x + 1 3 1 3
= 2.) -3 x = -2
3 4 2 5
1

2. 2

3. 3

4. Anticipatory Set
How do you think fractions and decimals will impact the
procedures for solving two-step equations.
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5. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
1 x + 13 20
=
6
5

6. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
3 p-7
= 11
4
6

7. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
2 x+2 = 3
5 4
7

8. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
2x 1
= -8
5 6
8

9. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
5 3 1
n- =
7 14 2
9

10. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
3 13 7
= e-
5 30 10
10

11. 3 13 7
= e-
5 30 10
11

12. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
1 m+ 1 4
=
3 6 9
12

13. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
2 x- 7 7
=
3 6 2
13

14. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
1 x-1 5
=
3 6
14

15. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
-2y 9
+ = 2
3 10
15

16. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
-15.3 = -7.5x + 55.2
16

17. ALGEBRA
The Search for Unknowns
Objective: Isolate the variable to find its value
RULES
1.) Keep the equation balanced
2.) Simplify each side by combining like terms and
using the distributive property.
3.) Move variable to one side using inverse operations.
4.) Use inverse operations
9.95 + 0.0035x = 12.75
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18. Before You Leave
For local telephone service, the McNeils pay $9.95 per month
plus $0.35 per minute for local calls. Last month, the paid
$12.75 for local service. Write and solve an equation to find
the minutes, m, of local calls.
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19. Mr. Tjersland's Math 7
Homework: Finish Class Notes
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