Math Test Review

1. Which graph represents

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Explanation

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2.

X > -3

X ≥ -3

X < -3

X ≤ -3

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Explanation

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3. Describe the solutions of

in words

All real numbers greater than 4

All real numbers greater than or equal to 2

All real numbers less than 2

All real numbers less than or equal to 4

The given answer states that the solutions are "all real numbers greater than or equal to 2." This means that any real number that is equal to or greater than 2 would be a solution to the equation. So, the set of solutions includes numbers like 2, 3, 4, 5, 6, and so on. Any number that is less than 2 would not be a solution to the equation.

Explanation

The given answer states that the solutions are "all real numbers greater than or equal to 2." This means that any real number that is equal to or greater than 2 would be a solution to the equation. So, the set of solutions includes numbers like 2, 3, 4, 5, 6, and so on. Any number that is less than 2 would not be a solution to the equation.

4. Cookies are sold in the lunchroom for $1.50. Ana wants to buy cookies for a group of her friends. If she has $20, which inequality can be solved to show the number of cookies c she can buy?

1.50c < 20

1.50c ≤ 20

1.50c > 20

1.50c ≥ 20

The inequality 1.50c ≤ 20 can be solved to show the number of cookies c that Ana can buy. This inequality states that the cost of the cookies, which is $1.50 multiplied by the number of cookies c, is less than or equal to $20. By solving this inequality, Ana can determine the maximum number of cookies she can buy with her $20.

Explanation

The inequality 1.50c ≤ 20 can be solved to show the number of cookies c that Ana can buy. This inequality states that the cost of the cookies, which is $1.50 multiplied by the number of cookies c, is less than or equal to $20. By solving this inequality, Ana can determine the maximum number of cookies she can buy with her $20.

5. $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mn»2«/mn»«/mfrac»«mo»§#8805;«/mo»«mn»8«/mn»«/math»$

D ≥ 4

D ≤ 4

D ≥ 16

D ≤ 16

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Explanation

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6. Which inequality represents the situation "no more than 160 students are in the freshmen class"?

S > 160

S ≥ 160

S < 160

S ≤ 160

The inequality s ≤ 160 represents the situation "no more than 160 students are in the freshmen class". This means that the number of students in the freshmen class (s) is less than or equal to 160.

Explanation

The inequality s ≤ 160 represents the situation "no more than 160 students are in the freshmen class". This means that the number of students in the freshmen class (s) is less than or equal to 160.

7. Solve -28 < 4y

Y < -7

Y > -7

Y < 7

Y > 7

The given inequality is -28 -7. Therefore, the correct answer is y > -7.

Explanation

The given inequality is -28 -7. Therefore, the correct answer is y > -7.

8. Which compound inequality is shown by the graph below?

X ≥ -3 AND x > 3

X ≥ -3 AND x < 3

X ≥ -3 OR x > 3

X ≥ -3 OR x < 3

The correct answer is x ≥ -3 AND x

Explanation

The correct answer is x ≥ -3 AND x

9. Which graph represents

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Explanation

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10. Solve the compound inequality

-5 ≤ m < 10

-2 ≤ m < 13

1 ≤ m < 16

6 ≤ m < 39

The correct answer is -5 ≤ m

Explanation

The correct answer is -5 ≤ m

11.

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»m«/mi»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mn»1«/mn»«mo».«/mo»«mn»5«/mn»«mo»§nbsp;«/mo»«mo»§#8804;«/mo»«mo»§nbsp;«/mo»«mn»4«/mn»«/math»

M ≤ -2.5

M ≥ -2.5

M ≤ 5.5

M ≥ 5.5

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Explanation

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12. Which graph represents the solutions of 1 + r > 3 OR r + 5 < 2?

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Explanation

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13.

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§nbsp;«/mo»«mo»(«/mo»«mn»1«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mi»h«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»§#8804;«/mo»«mo»§nbsp;«/mo»«mn»3«/mn»«mi»h«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»9«/mn»«/math»

H ≤ 1

H ≤ 2

No solutions

All real numbers

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Explanation

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14.

P ≥ 7

5 < p - 2

5 > p - 2

P ≤ 7

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Explanation

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15. $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mi»s«/mi»«mo»§nbsp;«/mo»«mo»§#8805;«/mo»«mo»§nbsp;«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mi»s«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»8«/mn»«/math»$

S ≥ 4

S ≥ 8

S ≥ 12

S ≥ 16

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Explanation

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16. Jasmine and her sister are saving to buy MP3 players. Jasmine has $50 and plans to save $10 per week. Her sister has $80 and plans to save $7 per week. In how many weeks will Jasmine have more money saved than her sister?

2 weeks

4 weeks

10 weeks

11 weeks

In 2 weeks, Jasmine will have saved $50 + ($10 * 2) = $70. Her sister will have saved $80 + ($7 * 2) = $94. In 4 weeks, Jasmine will have saved $50 + ($10 * 4) = $90. Her sister will have saved $80 + ($7 * 4) = $108. In 10 weeks, Jasmine will have saved $50 + ($10 * 10) = $150. Her sister will have saved $80 + ($7 * 10) = $150. In 11 weeks, Jasmine will have saved $50 + ($10 * 11) = $160. Her sister will have saved $80 + ($7 * 11) = $167. Therefore, in 11 weeks, Jasmine will have more money saved than her sister.

Explanation

In 2 weeks, Jasmine will have saved $50 + ($10 * 2) = $70. Her sister will have saved $80 + ($7 * 2) = $94. In 4 weeks, Jasmine will have saved $50 + ($10 * 4) = $90. Her sister will have saved $80 + ($7 * 4) = $108. In 10 weeks, Jasmine will have saved $50 + ($10 * 10) = $150. Her sister will have saved $80 + ($7 * 10) = $150. In 11 weeks, Jasmine will have saved $50 + ($10 * 11) = $160. Her sister will have saved $80 + ($7 * 11) = $167. Therefore, in 11 weeks, Jasmine will have more money saved than her sister.

17. Solve -4 (x - 1) < 12.

X > -2

X < -2

X > -3

The correct answer is x > -2. By solving the inequality, we can see that when we distribute -4 to (x - 1) and simplify the expression, we get -4x + 4 -2. Therefore, the answer is x > -2.

Explanation

The correct answer is x > -2. By solving the inequality, we can see that when we distribute -4 to (x - 1) and simplify the expression, we get -4x + 4 -2. Therefore, the answer is x > -2.

18. Mike is on a cross-country trip and wants to drive at least 450 miles per day. So far today, he has driven 175 miles. Which inequality can be solved to show the number of miles m that Mike must drive to meet his daily goal?

175 + m < 450

175 + m ≤ 450

175 + m > 450

175 + m ≥ 450

To find the number of miles Mike must drive to meet his daily goal, we need to set up an inequality. Since Mike wants to drive at least 450 miles per day, we use the greater than or equal to symbol. Adding the miles he has already driven today (175) to the number of miles he still needs to drive (m), we get the inequality 175 + m ≥ 450.

Explanation

To find the number of miles Mike must drive to meet his daily goal, we need to set up an inequality. Since Mike wants to drive at least 450 miles per day, we use the greater than or equal to symbol. Adding the miles he has already driven today (175) to the number of miles he still needs to drive (m), we get the inequality 175 + m ≥ 450.

19.

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«msup»«mn»2«/mn»«mn»3«/mn»«/msup»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mi»a«/mi»«mo»§nbsp;«/mo»«mo»§gt;«/mo»«mo»§nbsp;«/mo»«mo»-«/mo»«mn»3«/mn»«mo»(«/mo»«mn»2«/mn»«mo»-«/mo»«mn»6«/mn»«mo»)«/mo»«/math»

A < -6

A > -6

A < -4

A > -4

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Explanation

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20. John is considering accepting one of two sales positions. ABC Company offers a yearly salary of $45,000. XYZ Company offers a yearly salary of $38,000 plus a 2% annual commission on sales. For what amount of sales s is the salary at XYZ Company greater than the salary at ABC Company?

S > 7000

S > 35,000

S > 70,000

S > 350,000

In order for the salary at XYZ Company to be greater than the salary at ABC Company, the commission earned from sales at XYZ Company must exceed the difference in salaries between the two companies. The difference in salaries is $45,000 - $38,000 = $7,000. To find the amount of sales needed for the commission to exceed $7,000, we divide $7,000 by 2% (0.02) to get $350,000. Therefore, for the salary at XYZ Company to be greater, the amount of sales (s) must be greater than $350,000.

Explanation

In order for the salary at XYZ Company to be greater than the salary at ABC Company, the commission earned from sales at XYZ Company must exceed the difference in salaries between the two companies. The difference in salaries is $45,000 - $38,000 = $7,000. To find the amount of sales needed for the commission to exceed $7,000, we divide $7,000 by 2% (0.02) to get $350,000. Therefore, for the salary at XYZ Company to be greater, the amount of sales (s) must be greater than $350,000.

21.

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»7«/mn»«mo»§nbsp;«/mo»«mo»§lt;«/mo»«mo»§nbsp;«/mo»«mn»2«/mn»«/math»

X > -5

X < -5

X > 5

X < 5

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Explanation

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