AF4.0 Students solve simple linear equations and inequalities over the rational numbers. California Standards

Additional Examples 1A: Solving Equations with Decimals Solve. m + 4.6 = 9 m + 4.6 = 9 Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition. – 4.6 4.4 m = 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 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 Since p is multiplied by 8.2, divide both sides by 8.2. –32.8 8.2 8.2p 8.2 = –4 p =

Additional Examples 1C: Solving Equations with Decimals Solve. = 15 x 1.2 x 1.2 = 1.2 • 15 1.2 • Since x is divided by 1.2, multiply both sides by 1.2. x = 18

Check It Out! Example 1 Solve. A. m + 9.1 = 3 Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition. m + 9.1 = 3 –9.1 = –6.1 m = B. 5.5b = 75.9 Since b is multiplied by 5.5, divide both sides by 5.5. 75.9 5.5 5.5 5.5 = b 13.8 b =

C. Solve. Check It Out! Example 1C y 4.5 = 90 = 4.5 • 90 4.5 • Since y is divided by 4.5, multiply both sides by 4.5. y = 405

Additional Example 2A: Solving Equations with Fractions Solve. = – 3 7 n + 2 7 n + – = – – 3 7 2 7 27 2 7 Since is added to n, subtract from both sides. n = – 5 7

Additional Example 2B: Solving Equations with Fractions Solve. 1 6 2 3 y – = Since is subtracted from y, add to both sides. 1 6 = y – 2 3 1 6 + 1 6 + 1 6 = y 4 6 1 6 + Find a common denominator, 6. = y 5 6

Additional Example 2C: Solving Equations with Fractions Solve. 5 6 5 8 x = Since x is multiplied by , divide both sides by . 5 6 5 6 ÷ = ÷ 5 8 x 1 1 1 3 5 6 = 5 8 x 6 5 • Multiply by the reciprocal. Simplify. 1 1 4 1 x = 3 4

Solve. Check It Out! Example 2A 1 9 5 9 n + = – n + – = – – 5 9 1 9 19 Since is added to n, subtract from both sides. n = – 6 9 n = – 2 3 Simplify.

Solve. Check It Out! Example 2B = y – 1 2 3 4 Since is subtracted from y, add to both sides. 1 2 = y – 3 4 1 2 + 1 2 + 1 2 = y 3 4 2 4 + Find a common denominator, 4. = y 5 4 y = 1 1 4 Simplify.

Solve. Check It Out! Example 2C 3 8 3 4 x = Since x is multiplied by , divide both sides by . 3 8 3 8 ÷ = ÷ 3 4 x 1 1 1 2 3 8 = 3 4 x 8 3 • Multiply by the reciprocal. Simplify. 1 1 1 1 x = 2

Additional Example 3: Solving Word Problems Using Equations 1 3 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? Write an equation: Amount Saved Amount Needed  1/3 = 1 3 = a  $21.40

Additional Example 3 Continued Since a is multiplied by , divide both sides by . 1 3 = 21.40 ÷ a x ÷ 1 3 1 3 = 21.40  a   3 1 Multiply by the reciprocal. a = 64.20 Simplify. Janice needs to save $64.20.

Capacity of minivan’s tank Check It Out! Example 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 24 gallons of gasoline, how much gasoline can the tank in the minivan hold? 2 3 Write an equation: Capacity of minivan’s tank Capacity of car’s tank • 2/3 = 2 3 g • = 24

Check It Out! Example 3 Continued Since g is multiplied by , divide both sides by . 2 3 = 24 ÷ g  ÷ 2 3 2 3 = 24  g   3 2 Multiply by the reciprocal. g = 722 g = 36 Simplify. The minivan can hold 36 gallons of gas.