How to solve equations using:

• The Subtraction Property of Equality
• The Addition Property of Equality

Course 2, Lesson 6-1

• equation
• solution
• equivalent equations
• Subtraction Property of Equality
• Addition Property of Equality

Course 2, Lesson 6-1

Course 2, Lesson 6-1

Subtraction Property of Equality

Words The states that the two sides of an equation remain equal when you subtract the same number form each side.

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Symbols If a = b, then a – c = b – c

Subtraction Property of Equality

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Step-by-Step Example

1.

Solve x + 6 = 4. Check your solution.

x + 6 = 4

Write the equation.

– 6 = –6

Subtraction Property of Equality

x = –2

Simplify.

Check

x + 6 = 4

–2 + 6 = 4

4 = 4

Write the original equation.

Replace x with –2.

The sentence is true.

?

So, the solution is –2.

Answer

Need Another Example?

Solve 14 + y = 20. Check your solution.

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Step-by-Step Example

2.

Solve –5 = b + 8. Check your solution.

–5 = b + 8

Write the equation.

Subtraction Property of Equality

–13 = b

Simplify.

Check

–5 = b + 8

–5 = –13 + 8

–5 = –5

Write the original equation.

Replace x with –2.

The sentence is true.

?

So, the solution is –13.

–8 = –8

Answer

Need Another Example?

Solve –12 = 4 + c. Check your solution.

–16

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Step-by-Step Example

3.

An angelfish can grow to be 12 inches long. If an

angelfish is 8.5 inches longer than a clown fish,

how long is a clown fish?

12 = c + 8.5

Write the equation.

Subtraction Property of Equality

3.5 = c

Simplify.

A clown fish is 3.5 inches long.

–8.5 = –8.5

Words

Variable

Equation

An angelfish is 8.5 inches longer than a clown fish.

Let c represent the length of the clown fish.

12 = c + 8.5

Answer

Need Another Example?

A grapefruit weighs 11 ounces, which is 6 ounces more than an apple. Write and solve an equation to find the weight of the apple.

a + 6 = 11; 5 ounces

Course 2, Lesson 6-1

Addition Property of Equality

Addition Property of Equality

Words The states that the two sides of an equation remain equal when you add the same number to each side.

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Symbols If a = b, then a + c = b + c.

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Step-by-Step Example

4.

Solve x – 2 = 1. Check your solution.

x – 2 = 1

Write the equation.

Addition Property of Equality

x = 3

Simplify.

The solution is 3.

+ 2 = + 2

Check 3 – 2 = 1

Answer

Need Another Example?

Solve 12 = z − 8. Check your solution.

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Step-by-Step Example

5.

A pair of shoes costs $25. This is $14 less than the

cost of a pair of jeans. Find the cost of the jeans.

Shoes are $14 less than jeans. Let j represent the cost

of jeans.

Write the equation.

Addition Property of Equality

39 = j

Simplify.

The jeans cost $39.

+ 14 = + 14

25 = j – 14

Answer

Need Another Example?

Vivian practiced the piano for 32 minutes. She practiced 11 minutes less than her brother did. Write and solve an equation to determine how long her brother practiced the piano.

b − 11 = 32; 43 minutes

Write the steps�you would use�to solve x – 3 = 19.

Course 2 Lesson 6-1

Ratios and Proportional Relationships