AnswersAlgebra 1Solving Equations and Inequalities

Solving Equations and Inequalities — Test Answers

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1
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What is an equivalent equation solved for h ?

A
h is equal to the fraction with numerator p minus b and denominator 0 point 7 divided by r
B
h is equal to open paren p over 0 point 7 minus b close paren divided by r
C
h is equal to open paren p over 0 point 7 close paren divided by r minus b
D
h is equal to p over 0 point 7 minus b divided by r
2
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Which is an equivalent equation solved for y ?

A
y is equal to a minus pi x
B
y is equal to a divided by pi x
C
y is equal to a plus pi x
D
y is equal to a pi x y
3

What is the final step in solving the inequality negative 2 times open paren 5 minus 4 x close paren is less than 6 x minus 4 ?

A
x is less than negative 3
B
x is less than 3
C
x is greater than 3
D
x is greater than negative 3
4

What is the value of n in the equation 1 half times open paren n minus 4 close paren minus 3 is equal to 3 minus open paren 2 n plus 3 close paren ?

A
n is equal to 6
B
n is equal to 0
C
n is equal to 4
D
n is equal to 2
5

In order to be invited to tutoring or extension activities, a student's performance must be at least 20 points higher or lower than an average score. If the average score is 105 , which inequality represents p , the scores for students who are eligible for tutoring or extension activities?

A
p is less than 85 or p is greater than 125
B
p is less than or equal to 85 or p is greater than or equal to 125
C
85 is less than p comma p is less than 125
D
85 is less than or equal to p comma p is less than or equal to 125
6

Which number line represents the solutions to negative 2 absolute value of x is equal to negative 6 ?

A
Image with description A number line from negative 8 to positive 8 in increments of 1. Two points, one at negative 4 and one at positive 4.
B
Image with description A number line from negative 8 to positive 8 in increments of 1. Two points, one at negative 6 and one at negative 2.
C
Image with description A number line from negative 8 to positive 8 in increments of 1. Two points, one at negative 8 and one at negative 4.
D
Image with description A number line from negative 8 to positive 8 in increments of 1. Two points, one at negative 3 and one at positive 3.
7

The formula to convert °F to °C is C=59⁢(F−32). Convert 50 degree C to degree f

A
132 degree F
B
20 degree F
C
10 degree F
D
122 degree F
8

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

A
start absolute value x minus 45 end absolute value is equal to 3 ; minimum angle: 45 degrees
B
start absolute value x minus 45 end absolute value is equal to 3 ; minimum angle: 42 degrees
C
start absolute value x minus 3 end absolute value is equal to 45 ; minimum angle: 42 degrees
D
start absolute value x minus 3 end absolute value is equal to 45 ; minimum angle: 45 degrees
9

The volume, V, of a rectangular prism is determined using the formula V=l⁢w⁢h, where l is the length, w is the width, and h is the height of the prism. Using this formula, what is the width of a rectangular prism that has a volume of 138 point 2 4 cubic inches, a height of 9 point 6 inches, and a length of 3 point 2 inches? Round to the nearest tenth.

A
46 point 1 inches
B
414 point 7 inches
C
4 point 5 inches
D
0 point 2 inches
10

What is a correct first step in solving the inequality negative 4 times open paren 3 minus 5 x close paren is greater than or equal to negative 6 x plus 9 ?

A
negative 12 minus 20 x is greater than or equal to negative 6 x plus 9
B
negative 12 minus 20 x is less than or equal to negative 6 x plus 9
C
negative 12 plus 20 x is less than or equal to negative 6 x plus 9
D
negative 12 plus 20 x is greater than or equal to negative 6 x plus 9
11

Which situation could be represented by the graph? Open image in full-screen view

A
Babysitters earn between 8 dollars and 11 dollars per hour.
B
The dogs at a veterinary clinic are all 8 years old or under or are older than 11 years.
C
Students in the children’s choir are at least 8 years old but no more than 11 years old.
D
A program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months.
12

What value of x is in the solution set of 2 x minus 3 is greater than 11 minus 5 x ?

A
4
B
2
C
negative 3
D
0
13

What is the value of x in the equation 2 point 5 times open paren 6 x minus 4 close paren is equal to 10 plus 4 times open paren 1 point 5 plus 0 point 5 x close paren ?

A
13
B
13
C
2
D
12
14

The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation start absolute value x minus 72 point 5 end absolute value is equal to 4 What are the minimum and maximum temperatures in the house?

A
70 point 5 degrees Fahrenheit F and 74 point 5 degrees Fahrenheit F
B
68 point 5 degrees Fahrenheit F and 76 point 5 degrees Fahrenheit F
C
72 point 5 degrees Fahrenheit F and 74 point 5 degrees Fahrenheit F
D
72 point 5 degrees Fahrenheit F and 76 point 5 degrees Fahrenheit F
15

Deepak wrote out the steps to his solution of the equation 52−3⁢x−5+4⁢x=−74. Deepak's Solution Steps Resulting equations 1 Use the distributive property to simplify. 5 halves minus 5 plus 4 x minus 3 x is equal to negative 7 fourths 2 Simplify by combining like terms. negative 5 halves plus x is equal to negative 7 fourths 3 Use the addition property of equality. negative 5 halves plus 5 halves plus x is equal to negative 7 fourths plus 5 halves 4 Use multiplication to find equivalent fractions. negative 5 halves plus 5 halves plus x is equal to negative 7 fourths plus 10 fourths 5 Simplify by combining like terms. x is equal to 3 fourths Which step has an incorrect instruction?

A
Step 2
B
Step 4
C
Step 1
D
Step 3
16

Which input value produces the same output value for the two functions on the graph? f of x is equal to negative 2 thirds x plus 1 g of x is equal to 1 third x minus 2 Open image in full-screen view

A
x is equal to negative 3
B
x is equal to 3
C
x is equal to 1
D
x is equal to negative 1
17

In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours or after working more than 9 hours. How can this be written as a single compound inequality?

A
h is greater than 7 or h is less than 9
B
h is less than 7 or h is greater than 9
C
7 is less than h comma h is less than 9
D
7 is greater than h comma h is greater than 9
18

Solve the inequality. 2 times open paren 4 x minus 3 is greater than or equal to negative 3 times open paren 3 x close paren plus 5 x

A
left parenthesis negative infinity comma 0 point 5 right bracket
B
left parenthesis negative infinity comma 2 right bracket
C
x is greater than or equal to 2
D
x is greater than or equal to 0 point 5
19

Johan found that the equation negative 2 start absolute value 8 minus x end absolute value minus 6 is equal to negative 12 had two possible solutions: x is equal to 5 and x is equal to negative 11 Which explains whether his solutions are correct?

A
He is not correct because he made a sign error.
B
He is correct because both solutions satisfy the equation.
C
He is not correct because there is only one solution: x is equal to 5 .
D
He is not correct because there are no solutions.
20

When she adds 2 to both sides, the equation 4 x is equal to 3 x results. Which solution will best illustrate what happens to x ?

A
The equation has one solution: x is equal to 0 .
B
The equation has one solution: x is equal to 4 thirds .
C
The equation has infinite solutions.
D
The equation has no solution.

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