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Inequalities in One Variable Answers

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Austin solved an inequality and made an error. 3.5t – 2.75 ≤ 11.25 3.5t – 2.75 + 2.75 ≤ 11.25 + 2.75 3.5t ≤ 14 ≤ t ≥ 4

Question illustration
A
Austin made an addition error.
B
Austin made a division error.
C
Austin should not have changed the inequality sign.
D
Austin should have changed the inequality sign to <.
2
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The solution to an inequality is graphed on the number line.

Question illustration
A
{x | x < 4.5}
B
{x | x ≤ 4.5}
C
{x | x > 4.5}
D
{x | x ≥ 4.5}
3

What is the first step in solving the inequality 2x + 3 ≥ 17?

A
Divide the left side by 2.
B
Subtract 3 from both sides.
C
Change the direction of the inequality.
D
Change the inequality to >.
4

What is the solution to the inequality + 4 ≤ 0?

Question illustration
A
(–∞, –28)
B
(–∞, –28]
C
(28, ∞)
D
[28, ∞)
5

A phone plan has a limit of $25 that can be spent on text messages. The base cost of the text plan will cost a user $5. Each text will cost $0.05. How many text messages (t) can a user send without exceeding the plan limits?

A
t ≤ 400
B
t < 400
C
t ≤ 600
D
t < 600
6

Mrs. Valdez wanted to determine the number of people, p, she could safely take in her car to the fun run. She determined that p < 5.

A
Mrs. Valdez can take –2 people because –2 < 5.
B
Mrs. Valdez can take 2 people because 2 < 5.
C
Mrs. Valdez can take 3.5 people because 3.5 < 5.
D
Mrs. Valdez can take 5 people because 5 < 5.
7

Solve.5x – 10 ≤ 20

A
(–∞, 2]
B
(–∞, 2)
C
(–∞, 6]
D
(–∞, 6)
8

A family has $35 to spend on dinner. They spend $18 on entrees. Side dishes are $3 each. What is the greatest number of side dishes they can buy?

A
4
B
5
C
6
D
7
9

The solution to an inequality is given in interval notation as (2, ∞). What is another way to represent this solution set?

A
A number line going from negative 5 to positive 5. A solid circle appears at positive 2. The number line is shaded between positive 2 and negative 5.
Option A
B
A number line going from negative 5 to positive 5. An open circle appears at positive 2. The number line is shaded between positive 2 and negative 5.
Option B
C
A number line going from negative 5 to positive 5. A solid circle appears at positive 2. The number line is shaded between positive 2 and positive 5.
Option C
D
A number line going from negative 5 to positive 5. An open circle appears at positive 2. The number line is shaded between positive 2 and positive 5.
Option D
10

Which statement about solving inequalities is true?

A
Adding the same value to both sides of an inequality does not change the solution set.
B
Subtracting the same value from both sides of an inequality changes the solution set.
C
When dividing both sides of an inequality by the same positive value, it is necessary to reverse the inequality sign.
D
When multiplying both sides of an inequality by the same negative value, it is not necessary to reverse the inequality sign.

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