Math 6
Unit 4: One Step Equations and Inequalities
Study Guide
Name ___________________________________
Date _______________
Think It Out
1. Explain how the idea of a balance is used when solving equations.
Whatever you do to one side of the equation, you have to do the other.
2. What does an open circle mean on a number line? What does a closed circle mean on a number line?
Open Circle - Symbol used in graphing inequalities that shows that the number is NOT a possible answer for
the inequality
Closed circle – Symbol used in graphing inequalities that shows that the number is a possible answer for the
inequality
Equations
Solve AND check each equation.
3.
4.
m  5  12
4. n  2  15
-5 -5
+2 +2
5. 3z  39
3 z 39

3
3
z = 11
m=7
6.
w
5
8
8 w
( )  (5)8
1 8
w = 40
n = 17
7. Together a puppy and kitten weigh 15 ounces. Write an equation to represent the combined weight of the
p + k = 15
puppy, p, and the kitten, k.
8. The quarterback threw the football x yards over 4 plays. Write an expression to represent the quarterback’s
average yardage per play.
x
4
1
of the students in the
5
school, write and solve an equation to determine x, the number of students in the school.
9. Forty-five students chose to have their school pictures retaken. If this represents
1 45

5 X
10. Which problem situation matches the equation 12 x  240 ?
A. Jamie sold 240 newspaper subscriptions each month for 12 months. What is x, the total number of
newspaper subscriptions that Jamie sold in 1 year?
B. Brenna cycled a total of 240 miles this month. She cycled 12 miles less this month than last month.
What is x, the number of miles Brenna cycled last month?
C. Mary charges $12.00 per hour for labor to paint houses. What is x, the number of hours Mary worked
if she charged $240.00 for labor?
D. Sara bought 12 ride tickets and x game tickets. How many game tickets did she buy if she bought 240
tickets in all?
Inequalities
Solve, check and graph the solution to each inequality.
11.
3m  12
12. x  2  10
3m 12

3
3
-2
M>4
-2
x≤8
13. k  4  5
+4 +4
k<9
14.
g
9
2
𝑔
2( )
2
≥ (9)2
g ≥ 18
15. The weight limit on an elevator is 3,500 pounds. Passengers and cargo weighing a total of 2,450 pounds are
already on the elevator. Write an inequality that could be used to determine x, the possible additional weight
the elevator can carry.
X + 2450 ≤ 3500
16. Name two numbers that are a solution to the inequality 12  x ? Name two numbers that are NOT a solution to
the inequality 12  x ?
13, 14
17. Triangle ABC has side lengths of 3 units, 4 units, and x units. If each side of triangle ABC is doubled to create
triangle XYZ, how would you create an expression to represents the perimeter of new triangle XYZ?
2 (3 + 4 + x)
6 + 8 + 2x
2x + 14 units
18. Which table satisfies the equation y  x  4.5 ?
A.
B.
x
3
4
5
6
y
7.5
12
16.5
21
x
1
2
3
4
y
4.5
5.5
6.5
7.5
C.
D.
x
5
6
7
8
y
0.5
1.5
2.5
3.5
x
2
4
6
8
y
6.5
8.5
10.5
12.5
Cost ($)
19. The graph below shows the cost of gasoline at $3.50 per gallon.
Gasoline (gallons)
How would the graph change if the price changed to $2.00 per gallon?
A. The graph would be steeper.
B. The graph would be less steep.
C. The graph would stay the same.
D. The graph would begin at (0, 2).
20. Define the following terms:
a. Closed circle – Symbol used in graphing inequalities that shows that the number is a possible answer
for the inequality
b. Open Circle - Symbol used in graphing inequalities that shows that the number is NOT a possible
answer for the inequality
c. Greater than – Symbol used in graphing inequalities that shows that the value on the left side of the
inequality is larger than the value on the right side
d. Greater than or equal to – Symbol used in graphing inequalities that shows that the value on the left
side of the inequality is larger or the same value as the value on the right side
e. Less than – Symbol used in graphing inequalities that shows that the value on the left side of the
inequality is smaller than the value on the right side
f.
Less than or equal to – Symbol used in graphing inequalities that shows that the value on the left side
of the inequality is smaller or the same value as the value on the right side
g. Not equal to – Symbol used in graphing inequalities that shows that the value on the left side of the
symbol does not have the same amount as the value on the right side