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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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Warm Up Determine 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

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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 and Alex, Bridget and Henry

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

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**Vocabulary Addition Property of Equality Inverse operations**

Subtraction Property of Equality

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**To solve an equation means to find a solution to the equation**

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 – x + 5 = 8 7 – 3 = y = 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.

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**ADDITION PROPERTY OF EQUALITY**

Words Numbers Algebra You can add the same amount to both sides of an equation, and the statement will still be true. 2 + 3 = 5 2 + 7 = 9 x = y + z = + z x + z = y+ z

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**Use inverse operations when isolating a variable**

Use inverse operations when isolating a variable. Addition and subtraction are inverse operations, which means that they “undo” each other. 2 +5 7 7 5 2 = =

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**Additional Example 1: Using the Addition Property of Equality**

Solve the equation b – 7 = 24. Check your answer. b – 7 = 24 Think: 7 is subtracted from b, so add 7 to both sides to isolate b. b = 31 Check b – 7 = 24 31 – 7 = 24 ? Substitute 31 for b. 24 = 24 ? 31 is a solution.

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Check It Out: Example 1 Solve the equation y – 3 = 21. Check your answer. y – 3 = 21 Think: 3 is subtracted from y, so add 3 to both sides to isolate y. y = 24 Check y – 3 = 21 24 – 3 = 21 ? Substitute 24 for y. 21 = 21 ? 24 is a solution.

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**SUBTRACTION PROPERTY OF EQUALITY**

Words Numbers Algebra 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 x = y – z = – z x – z = y – z

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**Additional Example 2: Using the Subtraction Property of Equality**

Solve the equation t + 14 = 29. Check your answer. t + 14 = 29 Think: 14 is added to t, so subtract 14 from both sides to isolate t. – 14 – 14 t = 15 Check t + 14 = 29 = 29 ? Substitute 15 for t. 29 = 29 ? 15 is a solution.

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Check It Out: Example 2 Solve the equation x + 11 = 36. Check your answer. x + 11 = 36 Think: 11 is added to x, so subtract 11 from both sides to isolate x. – 11 – 11 x = 25 Check x + 11 = 36 = 36 ? Substitute 25 for x. 36 = 36 ? 25 is a solution.

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**Additional Example 3: Sports Application**

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? Let f represent the field goal points. 7 points field goal points = points scored f = 7 + f = 13 – – 7 Subtract 7 from both sides to isolate f. f = 6 They scored 6 points on field goals.

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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 point goals = points scored x = 3 + x = 23 – – 3 Subtract 3 from both sides to isolate x. x = 20 He scored 20 points from 2 point goals.

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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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Lesson Quiz Solve each equation. Check your answer. 1. x – 9 = 4 2. y + 6 = 72 3. 21 = n – 41 = w + 31 5. 81 = x – 102 x = 13; 13 – 9 = 4 y = 66; = 72 n = 62; 21 = 62 – 41 w = 96; 127 = x = 183; 81 = 183 – 102 6. 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

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**Lesson Quiz for Student Response Systems**

1. Solve the equation x – 11 = 5. Check your answer. A. x = 16; 16 – 11 = 5 B. x = 6; = 11 C. x = 55; 55 ÷ 11 = 5 D. x = 21; 21 – 11 = 5

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**Lesson Quiz for Student Response Systems**

2. Solve the equation 36 = n – 22. Check your answer. A. n = 58; 36 = 58 – 22 B. n = 12; = 36 C. n = 14; 22 = 36 – 14 D. n = 60; 36 = 60 – 22

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**Lesson Quiz for Student Response Systems**

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; = 15 D. z = 9; = 18

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**Lesson Quiz for Student Response Systems**

4. Solve the equation 143 = w Check your answer. A. w = 100; 143 = B. w = 110; 143 = C. w = 166; 143 = 166 – 33 D. w = 176; 143 = 33 – 176

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**Lesson Quiz for Student Response Systems**

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

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Some problems produce equations that have variables on both sides of the equal sign.

Some problems produce equations that have variables on both sides of the equal sign.

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