Unit 5
Chapter 5
Algebraic Equations
Name ______Class______
One Step Equations
An ______is a sentence stating that two quantities are equal. The value of a variable that makes an equation true is called the ______of the equation.
1. x + 6 = 4 2. –5 = b + 8
3. y + 6 = 9 4. x + 3 = 1
5. – 3 = a + 4 6. y – 3 = 4
7. r – 4 = – 2 8. q – 8 = – 9
9. A pair of shoes costs $25. This is $14 less than the cost of a pair of jeans. Find the cost of the jeans.
10. The average lifespan of a tiger is 17 years. This is 3 years less than the average lifespan of a lion. Write and solve an equation to find the average lifespan of a lion.
11. The highest recorded temperature in Warsaw, Missouri, is 118° F. This is 158° greater than the lowest recorded temperature. Find the lowest recorded temperature.
Multiplying or Dividing
The expression 3x means 3 times the value of x. The numerical factor of a multiplication expression like 3x is called a ______. So, 3 is the ______of x.
1. 20 = 4x 2. –8y = 24
3. 6x = – 30 4. –6a = 36
5. –9d = –72 6. 12x = –36
7. Lelah sent 574 text messages last week. On average, how many messages did she send each day?
8. Mrs. Acosta’s car can travel an average of 24 miles on each gallon of gasoline. Write and solve an equation to find how many gallons of gasoline she will need for a trip of 348 miles.
9. a-4= -9 10. y3=-8
11. m5=-7 12. 30=b-6
14. The distance d Tina travels in her car while driving 60 miles per hour for 3 hours is given by the equation d3=60 How far did she travel?
Solving Proportions
Solve proportions by cross multiplying.
a. x4=910 b. 234=5y c. 73=n21
d. After 2 hours, the air temperature had risen 7° F. Write and solve a proportion to find the amount
of time it will take at this rate for the temperature to rise an additional 13° F
e. The ratio of 7th grade students to 8th grade students in a soccer league is 17:23. If there are 204
students in all how many 7th are in 8th grade?
f. Olivia bought 6 containers of yogurt for $7.68. How much would Olivia pay for 10 yogurts at this
same rate?
g. Jaycee bought 8 gallons of gas for $31.12. What is the unit price? Write an equation that can be
used to find the cost (c) for the number of gallons (g) for any number of gallons? Use this equation
to find out how much Jayvee would pay for 11 gallons of gas.
h. Olivia typed 2 pages in 15 minutes. Write an equation relating the number of minutes (m) to the
number of pages (p) typed. How long will it take her to type 10 pages at this rate?
i. Trina earns $28.50 tutoring for 3 hours. How much would Trina earn tutoring for 2 hours? for 4.5 hours?
Rational Coefficients
1. 16 = 0.25n 2. .8m = 6.4
3. –.28p = 4.2 4. –4.7k = –10.81
5. 34x=1220 6. -79d=5
7. -34x=9 8. -78x=-2164
9. –2.5b = 20.5 10. -12=-518h
11. Valerie needs 23 yard of fabric to make each hat for the school play. Write and solve an equation to find how many hats she can make with 6 yards.
12. Three fourths of the fruit in a refrigerator are apples. There are 24 apples in the refrigerator. How many pieces of fruit are in the refrigerator?
Two Step Equations
A ______, such as 2x + 3 = 9, has two different operations, multiplication,
and addition. To solve a two-step equation, undo the operations in reverse order of the order of
operations.
Undo the addition or subtraction first.
Undo the multiplication or division.
Example
A company charges $2 for each balloon in an arrangement and a $3 delivery fee. You have $9 to
spend. The equation 2x + 3 = 9, where x is the number of balloons, represents the situation.
Work backward to solve for x.
Solve and check:
1. 3x + 2 = 23 2. –2y – 7 = 3
3. 4 + 15r= –1 4. 2x + 4 = 10
5. 3x + 5 = 14 6. 5 = 2 + 3x
7. 4x + 5 = 13 8. –5s + 8 = – 2
9. –2 + 23w = 10 10. 13 = 1 + 4s
11. –3y – 5 = 10 12. –7 = 1 + 23n
13. Toya had her birthday party at the movies. It cost $27 for pizza and $8.50 per friend for the movie tickets. How many friends did Toya have at her party if she spent $78?
14. Syreeta wants to buy some CDs that each cost $14, and a DVD that costs $23. She has $65. Write and solve an equation to find how many CDs she can buy.
15. Suppose your school is selling magazine subscriptions. Each subscription costs $20. The company pays the school half of the total sales in dollars. The school must also pay a one-time fee of $18. What is the fewest number of subscriptions that can be sold to earn a profit of $200?
TWO–STEP EQUATIONS
TWO–STEP EQUATIONS: Work Backwards
1) Find the VARIABLE.
2) Identify all operations.
3) In REVERSE ORDER of PEMDAS (SADMEP), cancel operations.
4) Use the same number and opposite operations
1. 2y – 7 = 23 2. 8 + 6x = – 4
3. –5r – 18 = 12 4. 11 – 7x = 67
Independent Practice
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13. 14.
15. 16.
17. 18.
SOLVING 2–STEP EQUATIONS WITH FRACTIONS
· Solve in reverse order of operations = SADMEP
· FRACTIONS represent DIVISION statements.
· Be careful for hidden parentheses when there are OPERATIONS in numerator
Option #1:NO OPERATIONS IN NUMERATOR / Option #2:
OPERATIONS IN NUMERATOR
PRACTICE PROBLEMS
1) 2)
3) 4)
5) 6)
More Two-Step Equations
1. 3(x+ 5) = 18 2. 4x+ 8-4 = 40
3. -5(x-10) = -35 4. -9x-4+ 5 = 86
5. 7(x+ 4.9) = 56 6. -12x+ 6.2-3 = 57
7. 23x+13=22 8. -79x+3+2=16
9. -47x-14=37 10. 58x-13=512
11. 8.3x+ 3.1+3= 86 12. -7.2(x- 15.6) = -9