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Math 78 Study Guide
Unit 4: Linear Equations in One variable
Name: _Key___________________
Knowledge and Understanding Math
1. What does absolute value represent?
The distance a number is from zero; the amount of spaces the number is from zero
on a number line; absolute value is always positive!
2. Explain the difference between an equation and an inequality.
An equation is equal to something whereas an inequality is not equal; an equation has
one exact solution whereas an inequality can have multiple/infinite solutions.
3. What are the possible solutions for an absolute value equation?
Two solutions: usually positive and negative; one solution; or infinite solutions (│x│=
x); no solution
Proficiency of Skills
4. Solve for m. -6m + 8 = -16
-8 -8
-6m = -24
-6
-6
M = 4
5. Solve for z. 36x + 12y – 3z = 81
-36x-12y
-36x-12y
-3z = 81 – 36x – 12y
-3
-3 -3
-3
Z = -27 + 12x + 4y
6. Solve for k. 6(k - 2) = 4k + 6
6k – 12 = 4k + 6
-4k
-4k
2k – 12 = 6
+12
+12
2k = 18
2
2
K = 9
7. Solve for x:
a.
x6 8
b. x  6  8
c. x  6  0
X = 2; x = -14
no solution
x = -6
8. Solve and graph the inequality. 6m – 32 ≤ 40
+32 +32
6m ≤ 72
6
6
M ≤ 12
•
4 5 6 7 8 9 10 11 12
Applications of Math
9. Write and solve the absolute value equation that represents the two numbers (x) that are 5
units away from 4 on a number line.
│x - 4│= 5
x = -1; x = 9
10. Diane has a gift card for $75. She has spent $16 already. Write an inequality to determine
the amounts that she can spend without exceeding the gift card amount. Then, solve and graph
the amount.
75 ≥ 16 + x
59 ≥ x
•
55 56 5758 5960 61 6263
Choose the best answer.
11. Write an inequality that best describes the following situation: Sara runs 30 minutes
everyday. In the 30 minute workout, she burns 200 calories. If Sara wants to burn 700
calories a week, how many days will she need to run?
X ≥ 700/200
12. Draw a graph that best displays the solution to this situation: Bob can spend $125 at Best
Buy. In his cart, he has movies that each cost $17. What is the number of movies he can buy
without exceeding his set amount?
125 ≥ 17x
7 ≥ x
Graph should have a closed dot on 7 and should be shaded to the left.
13. Solve 7(8 +5 h) = - 84
56 + 35h = -84
-56
-56
35h = -140
35
35
H = -4
14. What is the solution of 5 x  7  14  8 ?
-14 -14
5│x + 7│= -6
5
5
│x + 7│= -1.2
NO SOLUTION; THE ABSOLUTE VALUE CANNOT BE NEGATIVE
15. Solve. 2x+2 = 4x-6.
-2x -2x
2 = 2x – 6
+6
+6
8 = 2x
2
2
X = 4
16. Solve xy-5 = k for y.
+5 +5
Xy = k + 5
X
x
Y=k+5
x
17. Which statement can be modeled by x  3  12 ?
a. Jennie sold 3 cookbooks. To earn a prize, Jennie must sell at least 12 cookbooks.
b. Sam has 3 bottles of water. Together, Sam and Dave have at most 12 bottles of
water.
c. Peter has 3 baseball hats. Peter and his brothers have fewer than 12 baseball hats.
d. Kathy swam 3 laps in the pool this week. She must swim more than 12 laps.
18. The ball used in a soccer game may not weigh more than 16 ounces or less than 14 ounces at
1
the start of the match. After 1 ounces of air was added to the ball, the ball was approved for
2
use in the game. Write a compound inequality to show how much the ball might have weighed
before the air was added.
Please look at the corrected answer!!! I had it backwards!!!!
12 ½ ≤ x ≤ 14 ½
19. Businesses with profits less than $10,000 per year will be shut down. Write an inequality
that represents this situation.
X < 10,000