Answers Online Algebra Function Number AInequalities in One Variable

Inequalities in One Variable Answers

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

(–∞, –28)

(–∞, –28]

(28, ∞)

[28, ∞)

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Solve.5x – 10 ≤ 20

(–∞, 2]

(–∞, 2)

(–∞, 6]

(–∞, 6)

Solve.2a + 4 > 12

{a | a > 2}

{a | a > 4}

{a | a > 8}

{a | a > 10}

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?

Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30?

30n + 60 > 150

30n + 60 < 150

60n + 30 < 150

60n + 30 > 150

What is the best first step to solve the inequality 5x – 3 ≥ 2?

Add 3 to both sides of the equation.

Subtract 3 from both sides of the equation.

Add 2 to both sides of the equation.

Subtract 2 from both sides of the equation.

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?

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

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.

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.

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.

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.

The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.{n | n < 3}{n | n ≥ 3}(3, ∞)

{n | n < 3}

{n | n ≥ 3}

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.

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.

(3, ∞)

The solution to an inequality is graphed on the number line.

{x | x < 4.5}

{x | x ≤ 4.5}

{x | x > 4.5}

{x | x ≥ 4.5}

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

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.

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.

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.

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.

Which statement about solving inequalities is true?

Adding the same value to both sides of an inequality does not change the solution set.

Subtracting the same value from both sides of an inequality changes the solution set.

When dividing both sides of an inequality by the same positive value, it is necessary to reverse the inequality sign.

When multiplying both sides of an inequality by the same negative value, it is not necessary to reverse the inequality sign.

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

{n | n < 3}

{n | n ≥ 3}

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.

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.

(3, ∞)

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

Divide the left side by 2.

Subtract 3 from both sides.

Change the direction of the inequality.

Change the inequality to >.

Solve.5x – 10 ≤ 20

(–∞, 2]

(–∞, 2)

(–∞, 6]

(–∞, 6)

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?

t ≤ 400

t < 400

t ≤ 600

t < 600

30n + 60 > 150

30n + 60 < 150

60n + 30 < 150

60n + 30 > 150

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.

Mrs. Valdez can take –2 people because –2 < 5.

Mrs. Valdez can take 2 people because 2 < 5.

Mrs. Valdez can take 3.5 people because 3.5 < 5.

Mrs. Valdez can take 5 people because 5 < 5.