Download Study Guide unit 5

Unit 5 Study Guide
Name:______________________________
Date:________________Core:___________
Unit Goal: 8.EE Expressions & Equations
7. Solve linear equations in one variable.
a. Give examples of linear eqns in one variable with one soln, infinitely many solns, or no solns.
Show which of these possibilities is the case by successively transforming the given eqn into simpler
forms, until an equivalent eqn of the form x=a, a=a, or a=b results (where a & b are different numbers).
b. Solve linear eqns with rational number coefficients, including eqns whose solns require
expanding expressions using the distributive property and collecting like terms.
7
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1. What is the solution to the equation
15
(5x + 12)?
Show All Work Below
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2. How many solutions does an equation have when you isolate the variable and it equals a constant?
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3. A neighborhood Newspaper charges $22 for a membership plus an additional $2 for each newspaper. If Brea
visited bought the newspaper 7 times, how much did she pay to read their paper in total?
Show all work.
−8(5𝑥+12)
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4. Which is the solution to the equation
Show all work
3
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5. How many solutions does an equation have when the variable adds out and the final sentence is false?
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7. The basket weaving club is raising money to go to a basket weaving museum. So far they have raised $20 by
selling baskets for $2 each. If they need to raise a total of $300, how many more baskets do they need to sell?
Show all work
Sh
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8. Which is the solution to the equation x - 8 = 2 ( 3x-34)?
Show all work
Sho
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9. How many solutions does an equation have when the variable adds out and the final sentence is true?
____ 10. George is the youngest of four children. Fredrick is 10 years older than George, Burtha is twice as old as
Fredrick, and Brian is 5 years younger than Burtha. If George is 7 years old, how old is each of his siblings?
____ 11. Haley has $21,329 in a savings account. She wants to go on a trip to Costa Rica that costs $32,000. If she
earns $12 per hour at a part-time job, how many hours does she need to work to have enough money for her
trip?
____ 12.
How many solutions does the following equation have: 3x + 12x + 2 = 34 + 5x – 12?
____ 13. Mr. Brunner wants to buy a new video game that costs $62.00. Last week he saved $40 for the game. If he
earns $12 per hour at his part-time job, which equation can be used to find the number of hours, h, Mr.
Brunner needs to work to have enough money to buy the video game?
____ 14. Solve: -7p – 32 = 8p – 44 – 21p
____ 15. What is the solution of the equation 4(5x – 5) + 3x = 8(3x – 2)?
____ 16. What is the solution of the equation 5x (x-12) + 3x + 5 = 3x – 6 + 3(x+4)?
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____ 17. Solve 5x – 4 = 54 + 3x
____ 18. VanDerSloot’s Rentals charges $21.50 per hour to rent a surfboard and a wetsuit. Tater’s Surf Shop charges
$20.25 per hour to rent a surfboarf plus $1 extra for a wetsuit. What equation would you write to solve this
problem?
Solving Equations - Short Answer
Name:_____________________
1: Solve each equation
2: and determine whether the equation has no solution, one solution, or an inifinite number of solutions.
SHOW ALL OF YOUR WORK!
26. 11 + 3x– 7 = 6x + 5 – 3x
27. 𝟓(𝒙 − 𝟗) + 𝟑 = 𝟓𝒙 − 𝟒𝟐
28. 𝒙 − 𝟏 = 𝒙 + 𝟐 + 𝟐(𝒙 − 𝟐)