1-10 Solving Equations by Adding or Subtracting

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the Day

Lesson Quizzes

1-10 Solving Equations by Adding or Subtracting

Warm UpDetermine if the given numbers are solutions to the given equations.

1. x = 2 for 4x = 9

2. x = 5 for 8x + 2 = 42

3. x = 4 for 3(x – 2) = 10

no

yes

no

1-10 Solving Equations by Adding or Subtracting

Problem of the Day

Four couples have dinner together. The wives are Ginny, Helen, Sarah, and Bridget. The husbands are Mark, Alex, Stephen, and Henry. Who is married to whom?

• Sarah is Mark’s sister.

• Sarah introduced Henry to his wife.

• Bridget has 2 brothers, but her husband is an only child.

• Ginny is married to Stephen.

Ginny and Stephen, Helen and Mark, Sarah andAlex, Bridget and Henry

1-10 Solving Equations by Adding or Subtracting

Learn to solve one-step equations by using addition or subtraction.

1-10 Solving Equations by Adding or Subtracting

Vocabulary

Addition Property of EqualityInverse operationsSubtraction Property of Equality

1-10 Solving Equations by Adding or Subtracting

To solve an equation means to find a solution to the equation. To do this, isolate the variable—that is, get the variable alone on one side of the equal sign.

x = 8 – 5 x + 5 = 87 – 3 = y 7 = 3 + y

The variables are isolated. The variables are not isolated.

Recall that an equation is like a balanced scale. If you increase or decrease the weights by the same amount on both sides, the scale will remain balanced.

1-10 Solving Equations by Adding or Subtracting

You can add the same amount to both sides of an equation, and the statement will still be true.

2 + 3 = 5+ 4 + 4

2 + 7 = 9

ADDITION PROPERTY OF EQUALITYADDITION PROPERTY OF EQUALITY

Words Numbers Algebra

x = y+ z = + z

x + z = y+ z

1-10 Solving Equations by Adding or Subtracting

Use inverse operations when isolating a variable. Addition and subtraction are inverse operations, which means that they “undo” each other.

1-10 Solving Equations by Adding or Subtracting

Solve the equation b – 7 = 24. Check your answer.

Additional Example 1: Using the Addition Property of Equality

b – 7 = 24+ 7 +7

b = 31

Think: 7 is subtracted from b, soadd 7 to both sides to isolate b.

Check

b – 7 = 24

31 – 7 = 24?

24 = 24?

Substitute 31 for b.

31 is a solution.

1-10 Solving Equations by Adding or Subtracting

Check It Out: Example 1

Solve the equation y – 3 = 21. Check your answer.

y – 3 = 21+ 3 +3

y = 24

Think: 3 is subtracted from y, soadd 3 to both sides to isolate y.

Check

y – 3 = 21

24 – 3 = 21?

21 = 21?

Substitute 24 for y.

24 is a solution.

1-10 Solving Equations by Adding or Subtracting

You can subtract the same amount from both sides of an equation, and the statement will still be true.

4 + 7 = 11 –3 – 3

4 + 4 = 8

SUBTRACTION PROPERTY OF EQUALITYSUBTRACTION PROPERTY OF EQUALITY

Words Numbers Algebra

x = y– z = – z

x – z = y – z

1-10 Solving Equations by Adding or Subtracting

Solve the equation t + 14 = 29. Check your answer.

t + 14 = 29– 14 – 14

t = 15

Checkt + 14 = 29

15 + 14 = 29?

29 = 29?

Think: 14 is added to t, so subtract 14 from both sides to isolate t.

Substitute 15 for t.

15 is a solution.

Additional Example 2: Using the Subtraction Property of Equality

1-10 Solving Equations by Adding or Subtracting

Check It Out: Example 2

Solve the equation x + 11 = 36. Check your answer.

x + 11 = 36– 11 – 11

x = 25

Check

Think: 11 is added to x, so subtract 11 from both sides to isolate x.

x + 11 = 36

25 + 11 = 36?

36 = 36?

Substitute 25 for x.

25 is a solution.

1-10 Solving Equations by Adding or Subtracting

The Giants scored 13 points in a game against Dallas. They scored 7 points for a touchdown and the rest of their points for field goals. How many points did they score on field goals?

Additional Example 3: Sports Application

Let f represent the field goal points.

7 points + field goal points = points scored 7 + f = 13

7 + f = 13– 7 – 7

f = 6They scored 6 points on field goals.

Subtract 7 from both sides to isolate f.

1-10 Solving Equations by Adding or Subtracting

Check It Out: Example 3

A basketball player scored 23 points during a game. Of those points, 3 were from 3-point goals and the remainder were 2 point goals. How many points did he score with 2 point goals?

Let x equal the points scored by 2 point goals.

3 point goals + 2 point goals = points scored

3 + x = 23

3 + x = 23– 3 – 3

x = 20

He scored 20 points from 2 point goals.

Subtract 3 from both sides to isolate x.

1-10 Solving Equations by Adding or Subtracting

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

1-10 Solving Equations by Adding or Subtracting

Lesson Quiz

Solve each equation. Check your answer.

1. x – 9 = 4

2. y + 6 = 72

3. 21 = n – 41

4. 127 = w + 31

5. 81 = x – 102

y = 66; 66 + 6 = 72

x = 13; 13 – 9 = 4

n = 62; 21 = 62 – 41

w = 96; 127 = 96 + 31

x = 183; 81 = 183 – 1026. Tamika has sold 16 dozen cookies this week.

This was 7 dozen more than she sold last week. Write and solve an equation to find how many dozen cookies she sold last week.

x + 7 = 16; 9 dozen

1-10 Solving Equations by Adding or Subtracting

1. Solve the equation x – 11 = 5. Check your answer.

A. x = 16; 16 – 11 = 5

B. x = 6; 5 + 6 = 11

C. x = 55; 55 ÷ 11 = 5

D. x = 21; 21 – 11 = 5

Lesson Quiz for Student Response Systems

1-10 Solving Equations by Adding or Subtracting

2. Solve the equation 36 = n – 22. Check your answer.

A. n = 58; 36 = 58 – 22

B. n = 12; 12 + 22 = 36

C. n = 14; 22 = 36 – 14

D. n = 60; 36 = 60 – 22

Lesson Quiz for Student Response Systems

1-10 Solving Equations by Adding or Subtracting

3. Solve the equation z + 9 = 15. Check your answer.

A. z = 24; 24 – 9 = 15

B. z = 135; 9(15) = 135

C. z = 6; 6 + 9 = 15

D. z = 9; 9 + 9 = 18

Lesson Quiz for Student Response Systems

1-10 Solving Equations by Adding or Subtracting

4. Solve the equation 143 = w + 33. Check your answer.

A. w = 100; 143 = 100 + 33

B. w = 110; 143 = 110 + 33

C. w = 166; 143 = 166 – 33

D. w = 176; 143 = 33 – 176

Lesson Quiz for Student Response Systems

1-10 Solving Equations by Adding or Subtracting

5. A shop owner sold 27 books on Friday. This was 9 more than the number of books he sold on Thursday. Identify an equation and its solution that shows the number of books he sold on Thursday.

A. x + 27 = 36; 9 books

B. 9x = 27; 3 books

C. x + 9 = 27; 18 books

D. x – 9 = 27; 36 books

Lesson Quiz for Student Response Systems