# all 9

**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)

5. Solve. 8x + 2 = 7x

6. Solve. 7x – 0.96 = 6(x – 0.67)

7. Solve for x. 4x = –8

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

9. Solve for x. 35 – 7x = 35

10. Solve for x. – 5 = 5

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

12. Solve for x. 7x – 3 + 3x = 10x – 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

30. Solve -5x>23.5