AnswersAlgebra ISolving One-Variable Inequalities

Solving One-Variable Inequalities — Quiz Answers

10 verified answers
1
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Which is a correct first step in solving the inequality negative 4 times open paren 2 x minus 1 close paren is greater than 5 minus 3 x ?

A
Add 1 to both sides of the inequality.
B
Distribute negative 4 to get negative 8 x minus 1 is greater than 5 minus 3 x .
C
Distribute negative 4 to get negative 8 x plus 4 is greater than 5 minus 3 x .
D
Subtract 2 x from both sides of the inequality.
2
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Which number line represents the solution set for the inequality negative 1 half x is greater than or equal to 4 ?

A
Image with description A number line from negative 10 to positive 10 in increments of 2. A solid point is at negative 2 and a bold line starts at negative 2 and is pointing to the right.
B
Image with description A number line from negative 10 to positive 10 in increments of 2. A solid point is at negative 8 and a bold line starts at negative 8 and is pointing to the right.
C
Image with description A number line from negative 10 to positive 10 in increments of 2. A solid point is at negative 8 and a bold line starts at negative 8 and is pointing to the left.
D
Image with description A number line from negative 10 to positive 10 in increments of 2. A solid point is at negative 2 and a bold line starts at negative 2 and is pointing to the left.
3

Which number line represents the solution set for the inequality 3 times open paren 8 minus 4 x is less than 6 times open paren x minus 5 close paren ?

A
Image with description A number line from negative 5 to positive 5 in increments of 1. An open point is at positive 3 and a bold line starts at positive 3 and is pointing to the left.
B
Image with description A number line from negative 5 to positive 5 in increments of 1. An open point is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
C
Image with description A number line from negative 5 to positive 5 in increments of 1. An open point is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
D
Image with description A number line from negative 5 to positive 5 in increments of 1. An open point is at positive 3 and a bold line starts at positive 3 and is pointing to the right.
4

Which is a correct first step in solving 5 minus 2 x is less than 8 x minus 3 ?

A
2 minus 2 x is less than 8 x
B
5 is less than 6 x minus 3
C
5 is less than 10 x minus 3
D
3 x is less than 8 x minus 3
5

Which number line represents the solution set for the inequality 2 x minus 6 is greater than or equal to 6 times open paren x minus 2 close paren plus 8 ?

A
Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at negative 0 point 5 and a bold line starts at negative 0 point 5 and is pointing to the right.
B
Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at positive 0 point 5 and a bold line starts at 0 point 5 and is pointing to the right.
C
Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at positive 0 point 5 and a bold line starts at positive 0 point 5 and is pointing to the left.
D
Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at negative 0 point 5 and a bold line starts at negative 0 point 5 and is pointing to the left.
6

Which are correct representations of the inequality negative 3 times open paren 2 x minus 5 close paren is less than 5 times open paren 2 minus x close paren ? Choose two correct answers.

A
Image with description A number line from negative 7 to positive 3 in increments of 1. An open point is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
B
negative 6 x minus 5 is less than 10 minus x
C
x is less than 5
D
Image with description A number line from negative 3 to positive 7 in increments of 1. An open point is at positive 5 and a bold line starts at positive 5 and is pointing to the right.
E
negative 6 x plus 15 is less than 10 minus 5 x
7

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

A
x is greater than or equal to negative 2
B
x is greater than or equal to 3
C
x is less than or equal to negative 2
D
x is less than or equal to 3
8

What value of x is in the solution set of 3 times open paren x minus 4 close paren is greater than or equal to 5 x plus 2 ?

A
10
B
5
C
negative 10
D
negative 5
9

Which are correct representations of the inequality 6 x is greater than or equal to 3 plus 4 times open paren 2 x minus 1 close paren ? Choose three correct answers.

A
6 x is greater than or equal to 3 plus 8 x minus 4
B
Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at positive 0 point 5 and a bold line starts at positive 0 point 5 and is pointing to the right.
C
Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at positive 0 point 5 and a bold line starts at positive 0 point 5 and is pointing to the left.
D
Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at negative 0 point 5 and a bold line starts at negative 0 point 5 and is pointing to the right.
E
1 is greater than or equal to 2 x
10

Which number line represents the solution set for the inequality negative 4 times open paren x plus 3 close paren is less than or equal to negative 2 minus 2 x ?

A
Image with description A number line from negative 7 to positive 7 in increments of 1. A solid point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
B
Image with description A number line from negative 7 to positive 7 in increments of 1. A solid point is at positive 5 and a bold line starts at positive 5 and is pointing to the left.
C
Image with description A number line from negative 7 to positive 7 in increments of 1. A solid point is at positive 5 and a bold line starts at positive 5 and is pointing to the right.
D
Image with description A number line from negative 7 to positive 7 in increments of 1. A solid point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.

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