# Algebra: linear equations with fractions as coefficients

Please see the attached file for the fully formatted problems.

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

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#### Solution Summary

Solving linear equations by first eliminating the fractions or the decimal numbers.

Algebra Calculations

Can you please explain how to do these problems?

1. Evaluate 3x-4y/ 2z when x= -2, y=3, z=4 . Express your answer as a fraction.

2. Use the order of operations to simplify the following expression. (-2)2 -3 2

3. Write the statement as an algebraic equation: 'The difference between x and 2 is 4 more than twice x'

4. Name the property used in the equation: -2 (x+5) =-2x-10

5. Solve the following equation for x. 4(2x-3) +1= 6- 2 (x=4)

6. Solve the following equation for x.

2x+1/3 +3=4-(x+2)/2

7. After a 60% reduction, a pair of shoes sold for $30. What was the price of the shoes before the reduction?

8. Solve the following formula for r. I =Prt

9. Simplify the exponential expression. Express your answer with positive exponents. -2x -2y5 (3xy-3)

10. Simplify the exponential expression. Express your answer with positive exponents.

3x-2y2/(2x2y)3

11. For f(x) =2x2-5x =3 and g (x) =x+2 :

a. find (f + g)(x)

b. find (f + g)(2)

12. For f (x) =2x2 -5x+3 and g(x) =x+2 , find f(-2) + g (3) .

13. Use intercepts to graph the linear equation 3x + 5y = 14 . Label the intercepts on the graph.

14. Use the slope formula to find the slope of the line passing through the points

(-3, 7) and (4, -2). Then indicate whether the line through the points rises, fall, is horizontal, or is vertical.

15. Rewrite the equation 3x-4y =12 in slope-intercept form by solving for y. Then give the slope and y-intercept.

16. Find the equation of the line that has a slope of -3 and passes through (2, -5).

Write the equation in slope-intercept form.

17. Find the equation of the line passing through the point (-3, -3) that is perpendicular to the line 2x-y =4 . Write the equation in slope-intercept form.

18. Solve the following system of linear equations by substitution.

2x =3y=7

6x-y=1

Express the solution as a point (x, y). Check your result in both equations.

19. Solve the following system of linear equations by addition.

3x+5y=-17

2x-3y= -5

20. A company is planning to manufacture chairs. The fixed cost is $20,000 and the cost per chair is $40. Each chair will be sold for $80.

a. Write the cost function, C(x), of producing x chairs.

b. Write the revenue function, R(x), from the sale of x chairs.

c. Determine the break-even point. Describe what this means.