AnswersAZ-Algebra 1A MA101Solving One-Variable Inequalities

Solving One-Variable Inequalities — Unit test Answers

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Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?

A
6 + 2(x + 4) = (3 – x)
Option A
B
6 + 2(x + 4) = (x – 3)
Option B
C
(6 + 2)(x + 4) = (3 – x)
Option C
D
(6 + 2)(x + 4) = (x – 3)
Option D
2
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Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?

A
(x + 30 + 60) = x
Option A
B
(x) = x(30 + 60)
Option B
C
x(30 + 60) = x
Option C
D
(x) = (30 + 60)
Option D
3

At a pumpkin patch, if Armando guesses the weight of his pumpkin within 0.3 pounds, he gets to take the pumpkin home for free. If his pumpkin weighs 4.9 pounds, which two equations can be used to find the minimum and maximum weights he can guess in order to get his pumpkin for free?

A
x – 0.3 = 4.9 and x – 0.3 = –4.9
B
x + 0.3 = 4.9 and x + 0.3 = –4.9
C
x + 4.9 = 0.3 and x + 4.9 = –0.3
D
x – 4.9 = 0.3 and x – 4.9 = –0.3
4

Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. She spends of her paycheck on dinner with friends. If she had not earned the bonus, the amount she spent on dinner would have been of her paycheck. Which equation can be used to find h, the number of hours Lindsay worked last week?

Question illustration
A
(10h + 60) = (10h)
Option A
B
(10h + 60h) = (10h)
Option B
C
h(10 + 60) = h(10)
Option C
D
(10 + 60h) = (10h)
Option D
5

The solution is n = –2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification?

A
0.8 = 0.8
B
–0.8 = –0.8
C
3 = 3
D
–3 = –3
6

Solve the equation.–x + 8 + 3x = x – 6

A
x = –18
B
x = –14
C
x = 2
D
x = 4
7

How many solutions exist for the given equation?3(x + 10) + 6 = 3(x + 12)

A
zero
B
one
C
two
D
infinitely many
8

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s=180(n−2), where n is the number of sides.Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°? Round to the nearest whole number.

A
6 sides
B
7 sides
C
8 sides
D
9 sides
9

Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below.3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2

A
x=−6
B
x=−4
C
x=2
D
x=4
10

Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.What is the missing step of her solution?

Question illustration
A
Add 10.4 to both sides.
B
Add negative 10.4 to both sides.
C
Multiply both sides of the equation by 10.4.
D
Divide both sides of the equation by 10.4.
11

What is the value of p in the linear equation ?

Question illustration
A
−4
B
−2
C
2
D
4
12

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.

A
2.3p – 10.1 = 6.4p – 4
B
2.3p – 10.1 = 6.49p – 4
C
230p – 1010 = 650p – 400 – p
D
23p – 101 = 65p – 40 – p
E
2.3p – 14.1 = 6.4p – 4
13

Laurie is trying to stay within 10 feet of her current diving depth of –30 feet (with regard to sea level) so that the light is still good but she can be close to the sea life during her scuba dive. Which two equations can be used to find the minimum and maximum depths Laurie wants to stay between?

A
-30 - x = 10 and -30 - x = –10
B
-30 + x = 10 and -30 + x = –10
C
x + 10 = 30 and x + 10 = –30
D
x – 10 = 30 and x – 10 = –30
14

What is the solution to 3|–3x + 9| = –18?

A
x = –5
B
x = 5 or x = 1
C
x = –5 or x = 1
D
no solution
15

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

Question illustration
A
v +4 = 8 – v
Option A
B
v +4 = 8
Option B
C
4 + v = 8 – v
Option C
D
2v + 4 = 8
16

The formula for the area of a triangle is , where b is the length of the base and h is the height.Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.

Question illustration
A
3 units
B
5 units
C
8 units
D
9 units
17

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

Question illustration
A
v +4 = 8 – v
Option A
B
v +4 = 8
Option B
C
4 + v = 8 – v
Option C
D
2v + 4 = 8
18

Which number line represents the solution set for the inequality 3x < –9?

A
A number line from negative 4 to 4 in increments of 1. A point is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
Option A
B
A number line from negative 4 to 4 in increments of 1. A point is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Option B
C
A number line from negative 4 to 4 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
Option C
D
A number line from negative 4 to 4 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Option D
19

The axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.What is the equation when solved for a?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

Solve the equation.2x − 3 + 4x = 21

A
x = −12
B
x = −6
C
x = 4
D
x = 6

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