Bell Quiz

Objectives

• Solve one-step equations by addition and subtraction.

New Concept

• An equation is a statement that uses an equal sign to show that two quantities are equal.

• A solution of an equation in on variable is a value of the variable that makes the equation true.

Example 1Identifying Solutions

State whether the value of the variable is a solution of the equation

x + 6 = 9 for x = 3

Example 2 Identifying Solutions

State whether the value of the variable is a solution of the equation

x – 6 = 9 for x = 3

Lesson Practice

State whether the value of the variable is a solution of the equation

h – 14 = 2 for h = 12

Lesson Practice

State whether the value of the variable is a solution of the equation

–11 = j – 4 for j = – 7

Equivalent Equations

• An equation is like a balance scale.

• The scale remains balanced when the same quantity is added to both sides, or when the same quantity is subtracted from both sides.

• An equivalent equation has the same solution set.

Addition and Subtraction Properties of Equality

• By adding or subtracting the same quantity from both sides of an equation, each equation remains equivalent to the original equation

• Furthermore, each side of the equation remains balanced as the equation is solved.

• The Addition and Subtraction Properties of Equality hold for every real number a, b, and c.

Addition and Subtraction Properties of Equality

Addition Property of EqualityYou can add the same number to both sides of an equation and the statement will still be true.

Examples: 2 = 2 a = b 3 + 2 = 2 + 3 a + c = b + c 5 = 5

Subtraction Property of EqualityYou can subtract the same number from both sides of an equation and the statement will still be true.

Examples: 10 = 10 a = b 10 – 4 = 10 – 4 a – c = b – c 6 = 6

Inverse Operations

• An inverse operation is an operation that undoes another.

• To solve an equation, isolate the variable on one side of the equal sign by using inverse operation

Inverse Operations

Addition <------------> Subtraction

Multiplication <------------> Division

Example 3Solving Equations by Adding

Solve. Then check the solution.

x – 3 = 12

Example 4Solving Equations by Adding

Solve. Then check the solution.

–15 = n – 8

Lesson Practice

Solve. Then check the solution.

x – 5 = 17

Lesson Practice

Solve. Then check the solution.

– 30 = m – 12

Example 5 Solving Equations by Subtracting

Solve. Then check the solution.

k + 7 = 13

Example 6 Solving Equations by Subtracting

Solve. Then check the solution.

–21 = p + 9

Lesson Practice

Solve. Then check the solution.

p + 3 = 37

Lesson Practice

Solve. Then check the solution.

–14 = y + 8

Example 7Solve Fraction Equations by Adding or Subtracting

Solve.

x +14

– 38

=

Lesson Practice

Solve.

1d + 4

2= 3

16

Example 8Application: Weather

On January 10, 1911, the temperature in Rapid City, South Dakota fell 47°F in 15 minutes. What was the temperature if it fell to 8°F?

Lesson Practice

Sam took the same test twice. On the second test he scored 87, which was 13 points higher than on the first test. What was his first test score?