AnswersJunior Studies Math - A Mrs. Hitchcock 26-27Inequalities in One Variable

Inequalities in One Variable Answers

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The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.

Question illustration
A
{n | n < 3}
B
{n | n ≥ 3}
C
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
Option C
D
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.
Option D
E
(3, ∞)
2
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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
3

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.
4

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 >.
5

Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate’s problem?

A
The shelter can house 15.6 cats because 15.6 < 28.
B
The shelter can house –8 cats because –8 < 28.
C
The shelter can house 17 cats because 17 < 28.
D
The shelter can house 28 cats because 28 < 28.
6

Solve.2a + 4 > 12

A
{a | a > 2}
B
{a | a > 4}
C
{a | a > 8}
D
{a | a > 10}
7

Devin is collecting signatures for a petition to open a new park in her town. She needs to collect at least 1,000 signatures before she can schedule a meeting with the mayor. She already has 380 signatures. If each petition page holds 80 signatures, which inequality best shows how many more pages (p) Devin needs?

A
7 ≤ p
B
8 ≤ p
C
8 < p
D
9 < p
8

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.
9

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}
10

Xavier can work no more than 40 hours in a week. He has already worked 24 hours this week. What is the maximum number of 8-hour days Xavier can work for the rest of the week?

A
2
B
3
C
4
D
5

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