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# Algebra: linear equations with fractions as coefficients

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Use the appropriate property of equality to solve each equation.
91. 5a = -10
7

93. 1 v = - 1 v + 3
2 2 8

Solve each equation.

77. 7- 3(5 -u) = 5(u - 4)

85. 4 - 2n = 12
5

90. 3(x - 0.87) - 2x = 4.98

Solve each equation by first eliminating the fractions.

13. x + x = 20
2 3

21. 1 v +1 = 1 v - 1
6 4
Solve each equation by first eliminating the decimal numbers.

31. 0.1a - 0.3 = 0.2a - 8.3

Solve each equation.

53. -3x+ 1 = -1 - 2x

Solve each equation. Identify each as a conditional equation, an inconsistent equation, or an identity.

69. (3 - 3)(5 - z) = 0

Solve each equation for x.

31. 3x + 2ab = 4x - 5ab

Solve each equation for y.
53. y - 1 = - 1 (x - 1)
2 4 2

Fill in the tables using the given formulas.

71. S = n (n+1)
2

n S
1
2
3
4
5

82. Finding MSRP. What was the MSRP for a Hummer H1 that sold for \$107,272 after an 8% discount?

11. Consecutive odd integers. Two consecutive odd integers have a sum of 152. What are the integers?

122. Diversification. Helen has 15 of her portfolio in U.S. stocks, 18 of her portfolio in European stocks, and 110 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds. What fraction of her portfolio is invested in municipal bonds? What percent is invested in municipal bonds?

106. Net worth. Melanie's house is worth \$125,000, but she still owes \$78,422 on her mortgage. She has \$21,236 in a savings account and has \$9477 in credit card debt. She owes \$6131 to the credit union and figures that her cars and other household items are worth a total of \$15,000. What is Melanie's net worth?

DQ1
1. You would like to explain to your friend a general strategy for solving linear equations and inequalities in a very organized way.

DQ2
Prepare to discuss your findings and the necessary steps to solve for this problem.
1. Perimeter of a triangle. The perimeter of the triangle shown in the accompanying figure is 12 meters. Determine the values of x, x + 1, and x + 2 by solving the equation.
x + (x + 1) + (x+ 2) = 12.
2. Cost of a car. Jane paid 9% sales tax and a \$150 title and license fee when she bought her new Saturn for a total of \$16,009.50. If x represents the price of the car, then x satisfies x _ 0.09x _ 150 _ 16,009.50. Find the price of the car by solving the equation.

DQ3
Prepare to discuss your findings and the necessary steps to solve for this problem.
1. -2 < -2
2. -3 < 0 < -1
3. The graph of x < -3 includes the point at -3
4. The number -3 is a solution to -2 < x.

Quiz
Solve each equation.
1. 3(2x - 1) = 7 + 4x
2. - 2 z = - 4
3 5
3. 3 - 1/5 (x) = 2
4. 15 - 1z = 1z
4 4
5. 0.02x + x = 51
6. s - 2 = 0
6 9
7. 4x = 3x
8. 3 - 4x = 2(1 - 2x)

Solve for the indicated variable.
9. 4x + 3y = 6 Solve for y

10. PV = nRT Solve for T

11. 6(x - a) - (36b -x) = a - b Solve for x

12. James paid \$105 for a DVD player that was priced originally at \$140. What was the discount rate?

13. Christine paid \$12,640 for a car that was on sale for 20% off. What are the original prices?

14. True or False: - 5 < - 8

15. True or False: 13(8) - 36 > 7(10) - 6(5)

Solve the inequality and state the solution set using interval notation
16. 3 - 2x < 9

Write the appropriate inequality symbol in the blank so that the two inequalities are equivalent.

17. - 3n < 45
n ______ -15

18. - 1 x < 3
8
x ______ - 24

Solve each equation or inequality

19. x + 7(5 - x) = 4

20. (x/5) >= 2 or 3x >9