2Warm Up Solve. 1. x – 17 = 32 2. y + 11 = 41 x = 49 3. = 18 3. = 184. 12x = 1085. x – 9 = 20x = 49y = 30w5w = 90x = 9x = 29
3AF1.1 Write and solve one-step linear equations in one variable. CaliforniaStandards
4The slowest time in a 40-yard dash was 3 The slowest time in a 40-yard dash was 3.84 seconds slower than the fastest time of 7.2 seconds.You can write an equation to represent this situation.The slowest time s minus 3.84 is equal to the fastesttime of 7.2 seconds.s – 3.84 = 7.2
5Remember!You can solve an equation by performing the same operation on both sides of the equationto isolate the variable.
6Additional Example 1: Solving Equations by Adding or Subtracting Solve.Think: What is happening to the variable? How can I undo it?A. n – 2.75 = 8.3n – 2.75 = 8.30Since 2.75 is subtracted from n, add 2.75 to both sides.+ 2.75+ 2.75n = 11.05B. a = 42a = 42.00Since is added to a, subtract from both sides.–32.66–32.66a=9.34
7Check It Out! Example 1Solve.A. n – 1.46 = 4.7n – 1.46 = 4.70Since 1.46 is subtracted from n, add 1.46 to both sides.+ 1.46+ 1.46n = 6.16B. a = 36a = 36.00Since is added to a, subtract from both sides.–27.51–27.51a=8.49
8Additional Example 2A: Solving Equations by Multiplying and Dividing Solve.Same as x divided by 4.8x= 5.44.8x=5.44.8xSince x is divided by 4.8, multiply both sides by 184.108.40.206=5.4 4.84.8x = 25.92
9Additional Example 2B: Solving Equations by Multiplying and Dividing Solve.9 = 3.6d9 = 3.6d93.6dSince d is multiplied by 3.6, divide both sides by 3.6.=3.63.69=dThink: 9 ÷ 3.6 = 90 ÷ 363.62.5 = d
10 3.5 Check It Out! Example 2A Solve. x = 2.4 3.5 x = 2.4 3.5 x Since x is divided by 3.5, multiply both sides by 220.127.116.11=2.4 3.53.5x = 8.4
11Check It Out! Example 2BSolve.9 = 2.5d9 = 2.5d92.5dSince d is multiplied by 2.5, divide both sides by 2.5.=2.52.59=dThink: 9 ÷ 2.5 = 90 ÷ 252.53.6 = d
12Understand the Problem Additional Example 3: Problem Solving ApplicationA board-game box is 2.5 inches tall. A toy store has shelving measuring 15 inches vertically in which to store the boxes. How many boxes can be stacked in the space?1Understand the ProblemRewrite the question as a statement.Find the number of boxes that can be placed on the shelf.List the important information:• Each board-game box is 2.5 inches tall.• The store has shelving space measuring 15 inches.
13Additional Example 3 Continued 2Make a PlanThe total height of the boxes is equal to the height of one box times the number of boxes. Since you know how much vertical space the shelf has, you can write an equation with b being the number of boxes.2.5b = 15
14Additional Example 3 Continued Solve32.5b = 152.5b = 15Since b is multiplied by 2.5, divide both sides by 18.104.22.168.5b = 66 boxes can be stacked in the space.
15Additional Example 3 Continued 4Look BackYou can round 2.5 to 3 and estimate how many boxes will fit on the shelf.15 ÷ 3 = 5So 6 boxes is a reasonable answer.
16Understand the Problem Check It Out! Example 3A canned good is 4.5 inches tall. A grocery store has shelving measuring 18 inches vertically in which to store the cans. How many cans can be stacked in the space?1Understand the ProblemRewrite the question as a statement.Find the number of cans that can be placed on the shelf.List the important information:• Each can is 4.5 inches tall.• The store has shelving space measuring 18 inches.
17Check It Out! Example 3 Continued 2Make a PlanThe total height of the cans is equal to the height of one can times the number of cans. Since you know how much vertical space the shelf has, you can write an equation with c being the number of cans.4.5c = 18
18Check It Out! Example 3 Continued Solve34.5c = 184.5c = 18Since c is multiplied by 4.5, divide both sides by 22.214.171.124.5c = 44 cans can be stacked in the space.
19Check It Out! Example 3 Continued 4Look BackYou can round 4.5 to 5 and 18 to 20 estimate how many cans will fit on the shelf.20 ÷ 5 = 4So 4 cans is a reasonable answer.
20Lesson QuizSolve.1. x – = 19.5c = –103.323.4. m – = 14.355. The French Club is selling coupon books for $8.25 each. How many books must be sold to bring in $5,940?x = 33.73c = –8.2x= 6.1x = 56.739.3m = 27.32720 books