1. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers AF4.0 Students solve simple linear equations over the rational numbers. California Standards

2. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers m + 4.6 = 9 Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition. Once you have solved an equation, it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation. Remember! Additional Examples 1A: Solving Equations with Decimals Solve. 4.4 m = – 4.6 Notes

3. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 8.2p = –32.8 –4 p = Since p is multiplied by 8.2, divide both sides by 8.2. –32.8 8.2 8.2p 8.2 = Additional Examples 1B: Solving Equations with Decimals (Notes) Solve.

4. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Additional Examples 1C: Solving Equations with Decimals x = 18 Since x is divided by 1.2, multiply both sides by 1.2. = 15 x 1.2 = 1.2 15 1.2 Solve. Face Partners

5. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers m + 9.1 = 3 Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition. Check It Out! Example 1 –6.1 m = –9.1 = Solve. A. B. 5.5b = 75.9 75.9 5.55.5 = b 13.8 b = Since b is multiplied by 5.5, divide both sides by 5.5. Rally Coach

6. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers = 90 Check It Out! Example 1C y = 405 Since y is divided by 4.5, multiply both sides by 4.5. y 4.5 = 4.5 90 4.5 Solve. C. Notes

7. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Additional Example 2A: Solving Equations with Fractions = – 3737 n + 2727 n + – = – – 3737 2727 2727 2727 n = – 5757 Solve. 2727 Since is added to n, subtract from both sides. 2727 Notes

8. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 1616 = 2323 y – Additional Example 2B: Solving Equations with Fractions Find a common denominator, 6. =y 4646 1616 + = y – 2323 1616 Solve. Since is subtracted from y, add to both sides. 1616 1616 + 1616 + 1616 =y 5656 Notes

9. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 5656 = 5858 x 6565 6565 5656 = 5858 x Multiply by the reciprocal. Simplify. Additional Example 2C: Solving Equations with Fractions x = 3434 3 4 Solve. Since x is multiplied by, divide both sides by. 5656 5656 5656 ÷ = ÷ 5858 x 5656 5656 1 11 1 1 1 Notes

10. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 1919 = – 5959 n + Check It Out! Example 2A n = – 2323 Simplify. Solve. n + – = – – 5959 1919 1919 1919 n = – 6969 1919 Since is added to n, subtract from both sides. 1919 Elbow

11. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Check It Out! Example 2B y = 1 1414 Solve. Simplify. =y – 1212 3434 Find a common denominator, 4. =y 3434 2424 + = y – 3434 1212 Since is subtracted from y, add to both sides. 1212 1212 + 1212 + 1212 =y 5454 Elbow

12. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Check It Out! Example 2C Solve. 3838 = 3434 x 8383 8383 3838 = 3434 x Multiply by the reciprocal. Simplify. x = 2 2 1 Since x is multiplied by, divide both sides by. 3838 3838 3838 ÷ = ÷ 3434 x 3838 3838 1 1 1 11 1 Elbow

13. Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Write an equation: Amount Needed1/3 Amount Saved Additional Example 3: Solving Word Problems Using Equations  = Janice has saved $21.40. This is of what she needs to save to buy a new piece of software. What is the total amount that Janice needs to save? 1313 a 1313  = $21.40 4 Steps