AnswersFL-1200700-Mathematics for College Algebra MISSolving One-Variable Inequalities

Solving One-Variable Inequalities — Unit test Answers

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Working together, Rocco and Giulia can paint a room in 3 hours. It would have taken Rocco 7 hours to do the job alone. Which equation can be used to determine r, Giulia’s rate of work in parts per hour?

Question illustration
A
+ 3r = 7
Option A
B
+ 3r = 1
Option B
C
= r
Option C
D
= 3r
Option D
2
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Sarah drove 40 miles per hour. In 3 hours, Sarah drove 120 miles. Which is a valid proportion to represent this description?

A
StartFraction 40 over 1 EndFraction = StartFraction 120 over 3 EndFraction
Option A
B
StartFraction 1 over 40 EndFraction = StartFraction 120 over 3 EndFraction
Option B
C
StartFraction 40 over 3 EndFraction = StartFraction 120 over 1 EndFraction
Option C
D
StartFraction 1 over 40 EndFraction = StartFraction 120 over 3 EndFraction
Option D
3

The tables represent the functions f(x) and g(x).

Question illustration
A
x = –3
B
x = –1
C
x = 0
D
x = 1
4

What is the value of p in the proportion below?

Question illustration
A
2
B
10
C
40
D
72
5

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

A
–12 – 20x ≤ –6x + 9
B
–12 – 20x ≥ –6x + 9
C
–12 + 20x ≤ –6x + 9
D
–12 + 20x ≥ –6x + 9
6

Step 1: –10 + 8x < 6x – 4Step 2: –10 < –2x – 4Step 3: –6 < –2xStep 4: ________

A
x < –3
B
x > –3
C
x < 3
D
x > 3
7

Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.4(x – 1) – x = 3(x + 5) – 11 4x – 4 – x = 3x + 15 – 113x – 4 = 3x + 4

A
The equation has one solution: x = 0.
B
The equation has one solution: x = 8.
C
The equation has no solution.
D
The equation has infinite solutions.
8

What is the value of n in the equation ?

Question illustration
A
n = 0
B
n = 2
C
n = 4
D
n = 6
9

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse.

A
y = a · πx
B
y = a + (πx)
C
y = a – πx
D
y = a ÷ (πx)
10

Fiona solved the equation shown. – (6x – 3) = –

Question illustration
A
Simplify by combining like terms.
B
Simplify by using addition property of equality.
C
Simplify by using the multiplication property of equality.
D
Simplify by using the division property of equality.
11

The cost of toothpaste is $6.00 for 3 tubes. At this rate, how much do 12 tubes of toothpaste cost?

A
$15.00
B
$24.00
C
$36.00
D
$72.00
12

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b.

A
h = (– b)÷ r
Option A
B
h = – b ÷ r
Option B
C
h = ÷ r – b
Option C
D
h = ÷ r
Option D
13

How can you solve for x in the proportion ?

Question illustration
A
Set the sum of 7 and 8 equal to the sum of 24 and x, and then solve for x.
B
Set the sum of 7 and 24 equal to the sum of 8 and x, and then solve for x.
C
Set the product of 7 and 8 equal to the product of 24 and x, and then solve for x.
D
Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x.
14

What is the solution to the linear equation? + p = + p

Question illustration
A
p = 1
B
p = 2
C
p = 8
D
p = 10
15

Solve the equation.y + 3 = –y + 9

A
y = 1
B
y = 3
C
y = 6
D
y = 9
16

It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour.

A
3(2 – t) = 1.5t
B
3t = 1.5(2 – t)
C
3t + 1.5(2 – t) = 5
D
3(2 – t) + 1.5t = 5
17

On Monday, the Dairy Barn sold 14 waffle cones for every 6 sugar cones. On Tuesday, the Dairy Barn sold 7 waffle cones for every 3 sugar cones. Which proportion can be used to represent the cone sales?

A
StartFraction 14 over 6 EndFraction = StartFraction 3 over 7 EndFraction
Option A
B
StartFraction 14 over 6 EndFraction = StartFraction 7 over 3 EndFraction
Option B
C
StartFraction 6 over 14 EndFraction = StartFraction 7 over 3 EndFraction
Option C
D
StartFraction 3 over 7 EndFraction = StartFraction 14 over 6 EndFraction
Option D
18

A group of 32 players forms 4 volleyball teams. If there are 96 players, how many teams can be formed?

A
3 teams
B
8 teams
C
12 teams
D
24 teams
19

What is the value of x in the equation ?

Question illustration
A
StartFraction 2 Over 3 EndFraction left-parenthesis StartFraction one-half EndFraction. x plus 12 right-parenthesis equals left-parenthesis StartFraction one-half EndFraction left-parenthesis StartFraction one-third EndFraction x plus 14 right-parenthesis minus 3.
Option A
B
StartFraction one-half EndFraction left-parenthesis n minus 4 right-parenthesis minus 3 equals 3 minus left-parenthesis 2 n plus 3 right-parenthesis.
Option B
C
2
D
13
20

Sonny substituted 5 for x in the proportion and cross multiplied to get . Why is this?

Question illustration
A
because the cross sums of the proportion are equal
B
because the cross differences of the proportion are equal
C
because the cross products of the proportion are equal
D
because the cross quotients of the proportion are equal

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