Directions: Please show all of your work for each problem.  If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word.  There is a tutorial on using this equation editor in Module 1 Lecture Notes.  You also have the option of hand writing your work and scanning it.

 

1. Is 12 a solution to the equation 7 – x = 5?

 

2. Is –9 a solution to the equation 9 – 8x = 81?

 

3. Solve -2x+7>=9

 

4. Solve 3(x-5)<2(2x-1)

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5. Solve.&nbsp;&nbsp;&nbsp;&nbsp; 8x + 2 = 7x

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6. Solve.&nbsp;&nbsp;&nbsp;&nbsp; 7x – 0.96 = 6(x – 0.67)

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7. Solve for x.&nbsp;&nbsp;&nbsp;&nbsp; 4x = –8

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8. A company estimates that 5% of the parts they manufacture are defective.&nbsp; If 8 defective parts are found one week by the quality assurance testers, how many parts were manufactured that week?

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9. Solve for x.&nbsp;&nbsp;&nbsp;&nbsp; 35 – 7x = 35

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10. Solve for x.&nbsp;&nbsp;&nbsp; &nbsp;– 5 = 5

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11. Solve for x.&nbsp;&nbsp;&nbsp;&nbsp; 4(x – 2) + 4x = 5x + 4

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12. Solve for x.&nbsp;&nbsp;&nbsp;&nbsp; 7x – 3 + 3x = 10x – 3

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13. Solve for x.&nbsp;&nbsp;&nbsp;&nbsp; –10x + 1 – 7x = –17x + 7

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14. Solve the literal equation for y.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x + 5y = 25

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15. A rectangular solid has a base with length 5 cm and width 2 cm.&nbsp; If the volume of the solid is 100 cm3, find the height of the solid.&nbsp; [Hint: The volume of a rectangular solid is given by V = LWH.]

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16. Translate the following statement into an algebraic equation.&nbsp; Let x represent the number. &nbsp;1 less than 15 times a number is 9 times that same number.

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17. The sum of three consecutive odd integers is 201.&nbsp; Find the integers.

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18. At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 35 mi/hr.&nbsp; Two hours later, a second truck leaves along the same route, traveling at 70 mi/hr.&nbsp; When will the second truck catch up to the first?

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19. The base of an isosceles triangle is 1 in. less than the length of one of the equal sides.&nbsp; If the perimeter of the triangle is 20 in., find the length of each of the sides.

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20. Identify the amount in the statement “318 is 53% of 600.”

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21. Elaine was charged $126 interest for 1 month on a $1800 credit card balance.&nbsp; What was the monthly interest rate?

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22. A broach was marked up $150 from cost, which amounts to a 50% increase.&nbsp; Find the original cost of the broach.

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23. Solve the solution set.&nbsp;&nbsp;&nbsp; 8x + 3 < 4x – 13

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24. Solve the solution set.&nbsp;&nbsp;&nbsp; 5x + 12 > 10x – 8

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25. An arithmetic student needs an average of 70 or more to receive credit for the course.&nbsp; She scored 76, 69, and 84 on the first three exams.&nbsp; Write a simplified inequality representing the score she must get on the last test to receive credit for the course.

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26. The length of a rectangle is 2 in. more than twice its width.&nbsp; If the perimeter of the rectangle is 28 in., find the width of the rectangle.

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27. Solve and check: 6x=4(x-5)

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28. Solve 1/4x<=3/8

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29. Solve 8x-7<=7x-5

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30. Solve -5x>23.5