Download linear equations test review

Linear equations and graphing review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Use this balance-scales model to solve for x.
x
2
12
b. –10
a. 10
____
x
x
a. 15
____
c. –4
d. 9
c. 15
d. 25
12
b. 4
3. Solve this equation. 5t = 20
a. 4
b. 4
4. A black square represents 1 and a white rectangle represents the variable x.
Find the value of x.
a. –6
____
d. 6
2. Use this balance-scales model to solve for x.
x
____
c. 14
b. 2
5. Write an equation for this sentence.
4 added to 4 times a number is 57.
a. 4 + 4 = 57x
b. 4 + 4x = 57
c. –5
d. 2
c. 4  4x = 57
d. 4x + 4 = 57
____
6. Write an equation for this situation.
Each of 5 people contributed $y to buy a gift that costs $20.
a.
c.
b.
d.
____
7. Solve this equation. 4y + 8 = 36
a. 1
b. 3
c. 7
d. 24
8. Solve this equation.
a. +1
c. –24
d. –7
____
____
b. 7
9. Melissa has $300 to spend on school clothes.
She spends $100 on a coat and some sweaters that are on special for $20 each.
Solve the equation
to find the greatest number of sweaters s that Melissa can buy.
a. 15 sweaters
b. 11 sweaters
c. 9 sweaters
d. 10 sweaters
____ 10. Write an equation for this sentence.
A number divided by 2 is 11.
a.
b.
c.
d.
____ 11. Write an equation for this sentence.
The sum of 4 and one-third of a number is 9.
a.
b.
c.
d.
____ 12. Mimi thinks of a number. She divides the number by 4, then adds 2 to it. The answer is 21.
Write an equation for the problem.
a.
b.
c.
d.
____ 13. Solve this equation.
b. –13
c. 56
d. 10
____ 14. Expand.
a.
b.
c.
d.
____ 15. Expand.
a.
b.
c.
d.
____ 16. Which statement is correct?
i)
ii)
iii)
iv)
a. i
b. iii
c. ii
d. iv
____ 17. Solve this equation:
a. 5
b. –5
c.

____ 18. Solve this equation:
a. –3
b. 5
c.
9
5
a. 83
____ 19. Complete this table of values for the relation
x
1
2
3
d. 41
31
10
d. 20
.
4
y
a.
c.
x
1
2
3
4
x
1
2
3
4
y
3
6
9
12
y
2
1
0
–1
x
1
2
3
4
x
1
2
3
4
y
–4
–5
–6
–7
y
–3
–6
b.
d.
–9 –12
____ 20. Make a table of values for the relation
a.
for x = 1, 2, 3, and 4.
c.
x
1
2
3
4
x
1
2
y
–4
–5
–6
–7
y
–3
–6
x
1
2
3
4
x
1
2
3
4
y
–3
y
3
7
11
15
b.
3
4
–9 –12
d.
–7 –11 –15
____ 21. The ordered pair ( , 5) is in the linear relation with equation
Find the missing number in the ordered pair.
a. 3
b. 1
c. 6
3
.
d. –6
____ 22. Marsha works part-time in a coffee shop and earns $12 per hour.
An equation for this relation is
, where h represents the number of hours Marsha worked and w
represents her earnings in dollars. In one week Marsha earned $180.
How many hours did she work?
a. 14
b. 168
c. 16
d. 15
____ 23. Graph the relation y = –2x + 3 for integer values of x from 0 to 4.
y
y
a.
c.
4
3
2
1
0
–1
–2
–3
–4
b.
x
1 2 3 4 5
d.
y
2
1
0
–1
–2
–3
–4
–5
–6
3
2
1
0
–1
–2
–3
–4
–5
x
1 2 3 4 5
x
1 2 3 4 5
y
5
4
3
2
1
0
–1
–2
–3
x
1 2 3 4 5
____ 24. Complete the table of values for the linear relation
x
0
1
2
3
.
4
y
a.
c.
x
0
1
2
3
4
x
0
1
2
3
4
y
11
13
15
17
19
y
9
10
11
12
13
x
0
1
2
3
4
x
0
1
2
3
4
y
9
7
5
3
1
y
11
9
7
5
3
b.
d.
Short Answer
25. What is the mass needed to balance these scales?
6g
9g
8g
26. In the left pan of a set of balance scales, there are 3 identical unknown masses and a mass of 5 g.
The scales are balanced by placing a mass of 20 g in the right pan.
Find each unknown mass.
27. Match each equation in column 1 to to its solution in Column 2.
Column 1
Column 2
a)
i) x = 4
b)
ii) x = +4
c)
iii) x = +3
d)
iv) x = 3
28. Brandon wants to buy a stereo that costs $200. He has saved $90 and plans to save $10 each week.
a) Write an equation you can use to find how many weeks it will take Brandon to save enough money for the
stereo.
b) Solve the equation and solve the problem.
29. Solve this equation.
30. Solve this equation.
31. Which value, 4, 6, or 8, is the correct solution to the equation
32. Write an equation for this sentence, then solve the equation.
A number divided by 7 is 8.
? Explain.
33. Which pairs of expressions are equivalent?
a) 5(q + 4) and 5q + 4
b) 7(t + 8) and 7t + 56
c) 4(y + 5) and 4y + 9
d) 5(x + 8) and 5x + 40
34. Expand.
35. Solve this equation: 4(13 + x – 7) = 16
36. The equation of a linear relation is
. What is the value of y when x = 2?
37. The equation of a linear relation is
. What is the value of x when y = 34?
38. Make a table of values for the relation
for x = 0, 1, 2, 3, and 4.
39. The equation of a linear relation is
A(3, –1), B(7, –13), C(8, –16), D(9, –20)
. Which ordered pairs are NOT in the relation?
40. This table of values is for the linear relation with equation
Find the value of b.
x
1
2
3
4
5
y
7
6
5
4
3
41. The graph shows the relation
. Write the ordered pair for point P.
y
32
24
16
P
8
x
–4
–2
0
–8
–16
–24
–32
2
4
, where b is a constant.
42.The graph shows the relation
. Write the ordered pair for point Q.
y
24
16
8
x
–4
–2
0
2
4
–8
Q
–16
–24
43. The graph shows the linear relation
.
Describe the relationship between the variables x and y.
y
12
8
4
0
x
1 2 3 4 5
–4
–8
–12
44. Graph the relation
for integer values of x from 0 to 5.
Describe the relationship between the variables x and y in the graph.
45. Brandon has $240 in his bank account. He withdraws $25 each week.
An equation for this relation is
, where c represents the amount of money, in dollars, in
Brandon’s account after w weeks.
a) Complete this table of values for the relation.
Number of Weeks, w
0
2
4
6
Amount, c ($)
b) Find the amount of money in Brandon’s account after 7 weeks.
8
Problem
46. Sketch a balance-scales model to represent this equation:
Solve the equation for x. Show your work.
47. Solve this equation.
Show your work.
48. The 3 sides of a triangle measure x cm, (x + 5) cm, and (x + 4) cm.
If the perimeter of the triangle is 27 cm, find the side lengths of the triangle.
Show your work.
49. Expand.
Show your work.
50. Simplify this expression.
Show your work.
51. Simplify this expression.
Show your work.
52. The price of a calculator was reduced by $5.
Mr. Maxwell bought 32 calculators for use in his classroom.
The total cost of the calculators before taxes was $960.
What was the original price of the calculator?
Show your work.
53. Make a table of values for the relations
and
For what value of x will the relations have the same y-value?
.
54. Marie has $1140 in the bank. She withdraws $95 every month.
An equation for this relation is
.
a) What does c represent?
a) How much money will Marie have in her account after 8 months?
b) How long will it take Marie to withdraw all the money in her account?
Show your work.
55. A linear relation has this equation:
a) Make a table of values for x = 0, 2, 4, 6, and 8.
b) Graph the relation.
c) Find the value of x when y = 0.