Solving Equations by Multiplying 1 9 or Dividing

Solving Equations by Multiplying 1 -9 or Dividing Warm Up Write an algebraic expression for each word phrase. 1. A number x decreased by 9 x– 9 2. 5 times the sum of p and 6 5(p + 6) 2 + 8 n 4 __ 4. the quotient of 4 and a number c c 3. 2 plus the product of 8 and n

Solving Equations by Multiplying 1 -9 or Dividing Learn to solve equations using multiplication and division.

Solving Equations by Multiplying 1 -9 or Dividing You can solve a multiplication equation using the Division Property of Equality.

Solving Equations by Multiplying 1 -9 or Dividing Additional Example 1 A: Solving Equations Using Division Solve 6 x = 48 6 6 1 x = 8 x=8 Use the Division Property of Equality: Divide both sides by 6. 1 • x=x Check 6 x = 48 ? 6(8) = 48 Substitute 8 for x. ? 48 = 48

Solving Equations by Multiplying 1 -9 or Dividing Additional Example 1 B: Solving Equations Using Division Solve – 9 y = 45 – 9 1 y = – 5 Use the Division Property of Equality: Divide both sides by – 9. 1 • y=y Check – 9 y = 45 ? – 9(– 5) = 45 Substitute – 5 for y. ? 45 = 45

Solving Equations by Multiplying 1 -9 or Dividing Check It Out: Example 1 A Solve 9 x = 36 9 9 1 x = 4 x=4 Use the Division Property of Equality: Divide both sides by 9. 1 • x=x Check 9 x = 36 ? 9(4) = 36 Substitute 4 for x. ? 36 = 36

Solving Equations by Multiplying 1 -9 or Dividing Check It Out: Example 1 B Solve – 3 y = 36 Use the Division Property of Equality: Divide both sides by – 3 1 y = – 12 1 • y = y y = – 12 Check – 3 y = 36 ? – 3(– 12) = 36 Substitute – 12 for y. ? 36 = 36

Solving Equations by Multiplying 1 -9 or Dividing You can solve a division equation using the Multiplication Property of Equality.

Solving Equations by Multiplying 1 -9 or Dividing Additional Example 2: Solving Equations Using Multiplication b = 5. – 4 b = – 4 • 5 – 4 • – 4 b = – 20 Solve Check b =5 – 4 – 20 =? 5 – 4 ? 5 = 5 Use the Multiplication Property of Equality: Multiply both sides by – 4. Substitute – 20 for b.

Solving Equations by Multiplying 1 -9 or Dividing Check It Out: Example 2 c = 5. – 3 c = – 3 • 5 – 3 • – 3 c = – 15 Solve Check c =5 – 3 – 15 =? 5 – 3 ? 5 = 5 Use the Multiplication Property of Equality: Multiply both sides by – 3. Substitute – 15 for c.

Solving Equations by Multiplying 1 -9 or Dividing Additional Example 3: Money Application To go on a school trip, Helene has raised $670, which is one-fourth of the amount she needs. What is the total amount needed? fraction of amount raised so far 1 4 total amount needed = amount raised so far • x = 670 1 x = 670 Write the equation. 4 4 • 1 x = 4 • 670 Multiply both sides by 4. 4 Helene needs $2680 total. x = 2680 Check: The amount raised so far is about $700. She needs about 4 times this amount, or $2800. The answer is reasonable.

Solving Equations by Multiplying 1 -9 or Dividing Check It Out: Example 3 The school library needs money to complete a new collection. So far, the library has raised $750, which is only one-eighth of what they need. What is the total amount needed? fraction of total amount raised so far total amount needed 1 8 • x = = amount raised so far 750 1 x = 750 Write the equation. 8 8 • 1 x = 8 • 750 Multiply both sides by 8. 8 x = 6000 The library needs $6000 total. Check: The amount raised so far is about $800. She needs about 8 times this amount, or $6400. The answer is reasonable.

Solving Equations by Multiplying 1 -9 or Dividing Sometimes it is necessary to solve equations by using two inverse operations. For instance, the equation 6 x 2 = 10 has multiplication and subtraction. Variable term Multiplication 6 x 2 = 10 Subtraction To solve this equation, add to isolate the term with the variable in it. Then divide to solve.

Solving Equations by Multiplying 1 -9 or Dividing Additional Example 4: Solving a Two-Step Equation Solve 3 x + 2 = 14. Step 1: 3 x + 2 = 14 Subtract 2 to both sides to – 2 isolate the term with x in it. 3 x = 12 Step 2: 3 x = 12 Divide both sides by 3. 3 3 x=4

Solving Equations by Multiplying 1 -9 or Dividing Check It Out: Example 4 Solve 4 y + 5 = 29. Step 1: Step 2: 4 y + 5 = 29 Subtract 5 from both sides to – 5 isolate the term with y in it. 4 y = 24 Divide both sides by 4. 4 4 y=6

Solving Equations by Multiplying 1 -9 or Dividing Lesson Quizzes Standard Lesson Quiz

Solving Equations by Multiplying 1 -9 or Dividing Lesson Quiz Solve. 1. 3 t = 9 t=3 2. – 15 = 3 b b = – 5 3. x – 4 = – 7 x = 28 4. z ÷ 4 = 22 z = 88 5. A roller coaster descends a hill at a rate of 80 feet per second. The bottom of the hill is 400 feet from the top. How long will it take the coaster rides to reach the bottom? 5 seconds