2 1 Solving OneStep Equations Preview Warm Up

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2 -1 Solving One-Step Equations Preview Warm Up California Standards Lesson Presentation

2 -1 Solving One-Step Equations Preview Warm Up California Standards Lesson Presentation

2 -1 Solving One-Step Equations Warm Up Evaluate. 2 1. – 2 + 4

2 -1 Solving One-Step Equations Warm Up Evaluate. 2 1. – 2 + 4 1 3 3 3. 0. 96 ÷ 6 0. 16 5. 2. – 0. 51 + (– 0. 29) – 0. 8 4. (– 9) 81 1 Evaluate each expression for a = 3 and b = – 2. 6. a + 5 8 7. 12 b – 24

2 -1 Solving One-Step Equations California Standards Preparation for 5. 0 Students solve multistep

2 -1 Solving One-Step Equations California Standards Preparation for 5. 0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable, and provide justification for each step. Also covered: 2. 0

2 -1 Solving One-Step Equations Vocabulary equation solution of an equation solution set

2 -1 Solving One-Step Equations Vocabulary equation solution of an equation solution set

2 -1 Solving One-Step Equations An equation is a mathematical statement that two expressions

2 -1 Solving One-Step Equations An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. A solution set is the set of all solutions. Finding the solutions of an equation is also called solving the equation.

2 -1 Solving One-Step Equations To find solutions, perform inverse operations until you have

2 -1 Solving One-Step Equations To find solutions, perform inverse operations until you have isolated the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side. Inverse Operations Add x. Multiply by x. Subtract x. Divide by x. An equation is like a balanced scale. To keep the balance, you must perform the same inverse operation on both sides.

2 -1 Solving One-Step Equations

2 -1 Solving One-Step Equations

2 -1 Solving One-Step Equations Writing Math Solution sets are written in set notation

2 -1 Solving One-Step Equations Writing Math Solution sets are written in set notation using braces, { }. Solutions may be given in set notation, or they may be given in the form x = 14.

2 -1 Solving One-Step Equations Additional Example 1 A: Solving Equations by Using Addition

2 -1 Solving One-Step Equations Additional Example 1 A: Solving Equations by Using Addition or Subtraction Solve the equation. y – 8 = 24 +8 +8 y = 32 Since 8 is subtracted from y, add 8 to both sides to undo the subtraction. The solution set is {32}. Check y – 8 = 24 32 – 8 24 24 24 To check your solution, substitute 32 for y in the original equation.

2 -1 Solving One-Step Equations Additional Example 1 B: Solving Equations by Using Addition

2 -1 Solving One-Step Equations Additional Example 1 B: Solving Equations by Using Addition Solve the equation. 4. 2 = t + 1. 8 – 1. 8 2. 4 = t Check 4. 2 = t + 1. 8 4. 2 2. 4 + 1. 8 4. 2 Since 1. 8 is added to t, subtract 1. 8 from both sides to undo the addition. The solution set is {2. 4}. To check your solution, substitute 2. 4 for t in the original equation.

2 -1 Solving One-Step Equations Check It Out! Example 1 a Solve the equation.

2 -1 Solving One-Step Equations Check It Out! Example 1 a Solve the equation. Check your answer. n – 3. 2 = 5. 6 + 3. 2 Since 3. 2 is subtracted from n, add 3. 2 to both sides to undo the subtraction. n = 8. 8 Check The solution set is {8. 8}. n – 3. 2 = 5. 6 8. 8 – 3. 2 5. 6 To check your solution, substitute 8. 8 for n in the original equation.

2 -1 Solving One-Step Equations Check It Out! Example 1 b Solve the equation.

2 -1 Solving One-Step Equations Check It Out! Example 1 b Solve the equation. Check your answer. – 6 = k – 6 +6 +6 Since 6 is subtracted from k, add 6 to both sides to undo the subtraction. 0=k Check The solution set is {0}. – 6 = k – 6 – 6 0– 6 To check your solution, substitute 0 for k in the original equation.

2 -1 Solving One-Step Equations Check It Out! Example 1 c Solve the equation.

2 -1 Solving One-Step Equations Check It Out! Example 1 c Solve the equation. Check your answer. 6 + t = 14 Since 6 is added to t, subtract 6 – 6 from both sides to undo the addition. t= 8 Check 6 + t = 14 6 + 8 14 14 14 The solution set is {8}. To check your solution, substitute 8 for t in the original equation.

2 -1 Solving One-Step Equations

2 -1 Solving One-Step Equations

2 -1 Solving One-Step Equations Additional Example 2 A: Solving Equations by Using Multiplication

2 -1 Solving One-Step Equations Additional Example 2 A: Solving Equations by Using Multiplication or Division Solve the equation. Check your answer. Since j is divided by 3, multiply from both sides by 3 to undo the division. The solution set is {– 24}. – 24 = j Check To check your solution, substitute – 24 for j in the original equation. – 8

2 -1 Solving One-Step Equations Additional Example 2 B: Solving Equations by Using Multiplication

2 -1 Solving One-Step Equations Additional Example 2 B: Solving Equations by Using Multiplication or Division Solve the equation. Check your answer. – 4. 8 = – 6 v 0. 8 = v Check – 4. 8 = – 6 v – 4. 8 – 6(0. 8) – 4. 8 Since v is multiplied by – 6, divide both sides by – 6 to undo the multiplication. The solution set is {0. 8}. To check your solution, substitute 0. 8 for v in the original equation.

2 -1 Solving One-Step Equations Check It Out! Example 2 a Solve each equation.

2 -1 Solving One-Step Equations Check It Out! Example 2 a Solve each equation. Check your answer. p = 50 Check Since p is divided by 5, multiply both sides by 5 to undo the division. The solution set is {50}. To check your solution, substitute 50 for p in the original equation. 10 10

2 -1 Solving One-Step Equations Check It Out! Example 2 b Solve each equation.

2 -1 Solving One-Step Equations Check It Out! Example 2 b Solve each equation. Check your answer. 0. 5 y = – 10 y = – 20 0. 5 y = – 10 Check 0. 5(– 20) – 10 Since y is multiplied by 0. 5, divide both sides by 0. 5 to undo the multiplication. The solution set is {– 20}. To check your solution, substitute – 20 for y in the original equation.

2 -1 Solving One-Step Equations Check It Out! Example 2 c Solve each equation.

2 -1 Solving One-Step Equations Check It Out! Example 2 c Solve each equation. Check your answer. c = 56 Check Since c is divided by 8, multiply both sides by 8 to undo the division. The solution set is {56}. To check your solution, substitute 56 for c in the original equation. 7 7

2 -1 Solving One-Step Equations When solving equations, you will sometimes find it easier

2 -1 Solving One-Step Equations When solving equations, you will sometimes find it easier to add an opposite to both sides instead of subtracting or to multiply by a reciprocal instead of dividing. This is often true when an equation contains negative numbers or fractions.

2 -1 Solving One-Step Equations Additional Example 3 A: Solving Equations by Using Opposites

2 -1 Solving One-Step Equations Additional Example 3 A: Solving Equations by Using Opposites or Reciprocals Solve each equation. The reciprocal of is w is multiplied by both sides by . Since multiply . The solution set is {– 24}.

2 -1 Solving One-Step Equations Additional Example 3 B: Solving Equations by Using Opposites

2 -1 Solving One-Step Equations Additional Example 3 B: Solving Equations by Using Opposites or Reciprocals Solve each equation. Since p is added to , add to both sides to undo the subtraction. The solution set is. { }

2 -1 Solving One-Step Equations Check It Out! Example 3 a Solve the equation.

2 -1 Solving One-Step Equations Check It Out! Example 3 a Solve the equation. Check your answer. – 2. 3 + m = 7 +2. 3 + 2. 3 m = 9. 3 Check – 2. 3 + m = 7 – 2. 3 + 9. 3 7 7 7 Since – 2. 3 is added to m, add 2. 3 to both sides. The solution set is {9. 3}. To check your solution, substitute 9. 3 for m in the original equation.

2 -1 Solving One-Step Equations Check It Out! Example 3 b Solve the equation.

2 -1 Solving One-Step Equations Check It Out! Example 3 b Solve the equation. Check your answer. 5 +z= 4 Since is added to z add to both sides. The solution set is {2}. Check To check your solution, substitute 2 for z in the original equation.

2 -1 Solving One-Step Equations Check It Out! Example 3 c Solve the equation.

2 -1 Solving One-Step Equations Check It Out! Example 3 c Solve the equation. Check your answer. The reciprocal of is w is multiplied by both sides by w = 612 . Since multiply . The solution set is {612}. Check 102 To check your solution, substitute 612 for w in the original equation.

2 -1 Solving One-Step Equations Additional Example 4: Application Ciro deposits 1 of the

2 -1 Solving One-Step Equations Additional Example 4: Application Ciro deposits 1 of the money he earns from 4 mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find out how much money Ciro earned mowing lawns this year.

2 -1 Solving One-Step Equations Additional Example 4 Continued 1 4 times earnings e

2 -1 Solving One-Step Equations Additional Example 4 Continued 1 4 times earnings e is $285 = $285 Write an equation to represent the relationship. 4 1 4 4 is 1. 1, 4 The reciprocal of Since e e = 285 1 4 1 is multiplied by e = $1140 multiply both sides by 41. The original earnings were $1140.

2 -1 Solving One-Step Equations Check It Out! Example 4 The distance in miles

2 -1 Solving One-Step Equations Check It Out! Example 4 The distance in miles from the airport that a plane should begin descending divided by 3 equals the plane’s height above the ground in thousands of feet. A plane is 10, 000 feet above the ground. Write and solve an equation to find the distance from the airport at which this plane should begin descending.

2 -1 Solving One-Step Equations Check It Out! Example 4 Continued distance divided by

2 -1 Solving One-Step Equations Check It Out! Example 4 Continued distance divided by 3 is d ÷ 3 = height h Write an equation to represent the relationship. 3 d = 3 10 1 3 1 d = 30 1 Substitute 10 for h. The reciprocal of 3 is 31. Since d is multiplied by 13 multiply both sides by 31. At 10, 000 feet altitude the decent should start 30, 000 feet from the airport.

2 -1 Solving One-Step Equations Lesson Quiz Solve each equation. 1. r – 4

2 -1 Solving One-Step Equations Lesson Quiz Solve each equation. 1. r – 4 = – 8 – 4 3. 5. 2. 8 2. 4. 8 y = 4 40 6. This year a high school had 578 sophomores enrolled. This is 89 less than the number enrolled last year. Write and solve an equation to find the number of sophomores enrolled last year. s – 89 = 578; s = 667