7 S3c3po3 Solving Equations

Your Name (First & Last)

Bethune Junior High Math Solving & Creating Equations

Period 7S3C3 PO 6, 7S3C3 PO 3 7S3C3 PO 5, 8S3C3 PO 1

Date

Standard: 7S3C3 PO 6. Create and solve one-step inequalities with whole numbers. 7S3C3 PO 3. Solve multi-step equations using inverse properties with rational numbers. 7S3C3 PO 5. Create and solve two-step equations that can be solved using inverse operations with rational numbers. 8S3C3PO 1. Write or identify algebraic expressions, equations, or inequalities that represent a situation.

Objective: Students will be able to analyze real world situation, create algebraic equations, solve for variables, and check their work through substitution.

What does inverse mean?

Inverse Properties Additive

Multiplicative

Rule: Subtraction is the inverse operation of addition

Rule: Division is the inverse operation of multiplication

Directions: In each of the following identify the inverse operation. Ex: x – 3 = 1

4 (x) = 12

Inverse = Addition

Inverse =

y – 1.3 = 10.9

12 (m) = 144

Inverse =

Inverse =

3.5f = 45

W - 29 = - 45

Inverse =

Inverse =

t + 4 = 10

x = 7.5 2

Inverse =

Inverse =

Directions: Study the chart below & fill in the blanks with appropriate examples.

Expressions Equations Inequalities 2 2=2 2>1 5-3 5–3=2 5 – 3 > -1 4x 4x = 3 4x < 10 2(4x + y) 2(4x + y) = 0 2(4x + y) <1

This week we will be focusing on… EQUATIONS!

THE RULE OF EQUATIONS: WHATEVER YOU DO TO ONE SIDE OF AN EQUATON, YOU MUST DO TO THE OTHER!

Steps for solving one-step equations x – 4 = 5.5

1) Find the variable (Goal is to isolate variable)

Variable = x – 4 = 5.5

2) See what is being done to the variable

operation = x – 4 = 5.5 + +__

3) “Undo” what is being done by doing the opposite operation (do the INVERSE)

x=

4) Be sure to do it to both sides of the equation (balance).

____ – 4 = 5.5 5) Check answers! Use substitution.

Solve Solve for the Variable 1)

x – 3 = -2

2)

4x = -20

3)

x = -9 3

4)

*5)

p + 35 = -2

-x + 4 = 7

Check your work using substitution

Solving with Fractions

1)

1 x = 10 2

2)

2 w =
6 3

3)

3
x =
6 4

4)

3 x=9 2

Check your work using substitution

Write and solve 5 of your own one-step equations. Make sure you substitute the variable back in to check your work! 1 addition, 1 subtraction, 1 multiplication, 1 division

Steps for solving two-step equations 2x – 4 = 5.5

1) Find the variable (Goal is to Isolate Variable)

Variable = x 2x – 4 = 5.5

2) See what is being done to the variable

Subtraction/ Multiplication

2x – 4 = 5.5 + +__

2x 2

= ___ 2

x

= ___

2(___) – 4 = 5.5

3) “Undo” what is being done by doing the opposite operation (do the INVERSE) in reverse order of operations

4) Be sure to do it to both sides of the equation (balance)

5) Check Answers! Use substitution.

Examples: Solve x – 4 = 24 2

6b +10 = 4

Check

Solve for the Variable 1)

5x – 3 = -2

2)

-4x + 3 = -20

3)

x + 2 = -9 3

4)

*5)

5p + 32 = -2

-3x + 5 = 7

Check your work using substitution

Directions: Create, solve, and check your work for 4 two-step equations.

Solve for the Variable

Check your work using substitution