# Solving Multi-Step Equations

## Presentation on theme: "Solving Multi-Step Equations"— Presentation transcript:

Solving Multi-Step Equations
An alligator hatchling 6 inches long grows about 12 inches per year. The expression 12a + 6 represents the length in inches of an alligator that is "a" years old. ·What does the number 6 represent in the expression 12a + 6? ·What does the 12a represent in the expression 12a + 6? ·What does this expression assume about the growth of an alligator over its lifetime? ·How old is the alligator if it is 11 feet 6 inches long? 7m - 17 = a - 6 = = 3r t/ = 14

1 5q - 13 = 27

2 4g - 2 = -6

3 18 = 5p + 3

4 9 = 1 + m/7

5 (3/2)a - 8 = 11

·(p - 15)/9 = p = -39 ·(k - 12)/5 = k = 32 ·(n + 1)/ -2 = n = - 31

1 20 = (n - 3)/8

2 (b + 4)/ -2 = - 17

Allen is buying a pair of water skis that are on sale for 2/3 of the original price. After he uses a \$25 gift certificate, the total cost before taxes is \$115. What was the original price of the skis? Write an equation for the problem and solve. (2/3)p - 25 = 115 p = \$210

Susan had a \$10 coupon for the purchase of any item
Susan had a \$10 coupon for the purchase of any item. She bought a coat that was on sale for ½ its original price. After using the coupon, Susan paid \$125 for the coat before taxes. What was the original price of the coat? Write and solve and equation. (½)p - 10 = 125 p = \$270

Alex belongs to the Student Music Club and bought a discount card for \$ After one year, Alex has spent \$ Each CD cost \$3.95. Write and solve an equation to find how many CDs Alex bought during the year. Total Cost = Cost of CDs + Cost of Discount Card 63.40 = 3.95C Solve. 11 = C, or Alex bought 11 CDs during the year.

Sara paid \$15. 95 to become a member at a gym
Sara paid \$15.95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was \$ How much was the monthly fee? Total Cost = Monthly Fee + Membership Fee = 12 F Solve. F = 60, or Sara paid \$60 each month.

Lynda has 12 records in her collection
Lynda has 12 records in her collection. She adds the same number of new records to her collection each month. After 7 months Lynda has 26 records. How many records does Lynda add each month? Total Number = Number Added each month + Original Number 26 = 7R + 12 Solve. R = 2, or Lynda adds 2 new records each month.

Jan joined the dining club at the local cafe for a fee of \$29. 95
Jan joined the dining club at the local cafe for a fee of \$ Being a member entitles her to save \$2.50 every time she buys lunch. Jan calculates that she has saved a total of \$12.55 so far by joining the club. Writes and solve an equation to find how many times Jan has eaten lunch at the cafe. Total Savings = Savings each time - Original Fee = 2.50x Solve. x = 17, or Jan has eaten lunch 17 times at the cafe.

1 Twelve decreased by twice a number equals Write and solve an equation. A 23 B 35 C 92 D 17.5

2 The English alphabet contains 2 more than twice as many letters as the Hawaiian alphabet. How many letters are there in the Hawaiian alphabet?

Simplify Before Solving
Justify each step 6x x = 13 6x - 8x + 3 = 13 Commutative (6x - 8x) + 3 = 13 Associative x(6-8) + 3 = 13 Distributive -2x + 3 = 13 Sub. Prop of Equality -2x = 10 /-2 /-2 Div. Prop of Equality x = -5

Simplify Before Solving
Justify each step 2a a = 8 a = (-5/6)

Simplify Before Solving
Justify each step -8 - 2d + 2 = 4 d = -5

Simplify Before Solving
Justify each step 4x x = 40 x = 8

Simplify Before Solving
Justify each step 8x x = -15 x = 2

Simplify Before Solving
Justify each step 4 = 2x x x = (1/4)

Write and Solve an equation for the following problem.
Find three consecutive even integers whose sum is -42. Let n = the least even integer Then n + 2 = the next greater even integer and n + 4 = the greatest of the three even integers. n + (n + 2) + (n + 4) = - 42 n = -16 -16, -14, -12

Consecutive Integers Grade: Subject: Algebra Date:

Find three consecutive integers with a sum of 42
1 Find three consecutive integers with a sum of 42 A 12,13,14 B 13,14,15 C 14,15,16

Find three consecutive even integers with a sum of -12
-2, 0, 2 B -4, -2, 0 C -6, -4, -2

3 What is the greatest integer for the following: Find three consecutive odd integers whose sum is 57.

Simplifying Using the Distributive Property
Math Is Everywhere!.mp3 Simplifying Using the Distributive Property 9 = 6 - (x + 2) 9 = 6 + (-1)x + (-1)2 9 = x + -2 9 = (6-2) + -1x 9 = 4 - x 5 = -x -5 = x

Simplifying Using the Distributive Property
4(x + 1) + 2( x - 7) = 50 4x + 4(1) + 2x + 2(-7) = 50 4x x = 50 (4x + 2x) + (4 - 14) = 50 6x - 10 = 50 x = 10

Simplifying Using the Distributive Property

Simplifying Using the Distributive Property
10y - (4y + 8) = -20 y = -2

Distributive Property

1 5(2y - 7) + 8(y + 6) = 31

2 4x - 3(6 + x) - 1 = 2

3 17 - (4 - 6z) + 4 = 42

4 42r - 2(13 - 5r) + 7 = 85

5 3(x - 2) - 5(2x + 1) = 3

Attachments Math Is Everywhere!.mp3