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**Solving Equations by**Multiplying or Dividing 2-2 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1**2**3 Warm Up Evaluate each expression (#1-4). 1. (–7)(2.8) 2. 0.96 ÷ 6 3. 4. 19.6 5. Write an equation to represent the relationship. Then solve the equation: 0.16 Ten less than a number is equal to 12. n – 10 = 12 n=22 6. The angles in the diagram are Complementary (add to 90º). Write and solve an equation to find the value of x. 1 x + 42 = 90 x=48**Objective**Solve one-step equations in one variable by using multiplication or division.**Solving an equation that contains multiplication or division**is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable. Multiplication Division Division Multiplication**j**–8 = 3 –24 3 j –8 = Check 3 –8 Example 1A: Solving Equations by Using Multiplication Solve the equation. Since j is divided by 3, multiply both sides by 3 to undo the division. –24 = j To check your solution, substitute –24 for j in the original equation. –8 –8 **n**= 2.8 6 n = 2.8 Check 6 16.8 2.8 6 Example 1B: Solving Equations by Using Multiplication Solve the equation. Since n is divided by 6, multiply both sides by 6 to undo the division. n = 16.8 To check your solution, substitute 16.8 for n in the original equation. 2.8 2.8 **Check 9y = 108**Example 2A: Solving Equations by Using Division Solve the equation. Check your answer. 9y = 108 Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = 12 To check your solution, substitute 12 for y in the original equation. 9(12) 108 108 108 **Check –4.8 = –6v**Example 2B: Solving Equations by Using Division Solve the equation. Check your answer. –4.8 = –6v Since v is multiplied by –6, divide both sides by –6 to undo the multiplication. 0.8 = v –4.8 –6(0.8) To check your solution, substitute 0.8 for v in the original equation. –4.8 –4.8 **Remember that dividing is the same as multiplying by the**reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.**6**5 6 5 6 5 6 5 The reciprocal of is . Since w is multiplied by , multiply both sides by . 5 w = 20 Check 6 20 Example 3A: Solving Equations That Contain Fractions Solve the equation. 5 w= 20 6 w = 24 To check your solution, substitute 24 for w in the original equation. 2020 **3**2 1 3 3 8 1 1 3 16 16 8 8 2 The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. = z 3 16 1 Check = z To check your solution, substitute for z in the original equation. 8 Example 3B: Solving Equations That Contain Fractions Solve the equation. 3 = z 16 **1**Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. 4 Example 4: Application one-fourth times earnings equals college fund Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns. m = $1140**8**8 = a a 4 4 = c c WORDS Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the statement will still be true. NUMBERS 8 = 8 2 = 2 ALGEBRA a = b (c ≠ 0) Properties of Equality**Assignment**• L2-2 pg 87 #20-104x4**Lesson Quiz: Part 1**Solve each equation. 1. 2. 3. 8y = 4 4. 126 = 9q 5. 6. 21 2.8 –14 40**7. A person's weight on Venus is about his or her**weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus. 9 10 Lesson Quiz: Part 2