# Basic algebra problems

See the attached file.

Show all of your work. Circle your answer(s).

Chapter 1

1. Simplify: -12 + 5 - (-4) - 6

2. Simplify:-22(-3)2(5)

3. Simplify: 5/6 - 2/3 - 8/9

4. Simplify: 31.24 - 8.12 + 1.07

5. Simplify: (.8)(-2.4)(-3.8)

Chapter 2

6. Solve: -4 = x - 11

7. Solve: 8/15 = x + 2/5

8. Solve: -4/3y = 16/27

9. Solve: 7x -3(2x-4)=4(2-x)

10. Find the selling price per pound of a tea mixture made from 20 lbs. of tea costing $8.00 per pound and 80lbs of tea costing $3.40 per pound.

Chapter 3

11. Find the slope of the line containing the points P1(-2,3) and P2(1,-4)

12. Find the y-intercept of the line 3x +2y=-6

13. Find the equation of the line that contains the point (-1,4) and has slope -2

14. Find the equation of the line that contains the point (-1,-2) and has an undefined slope

15. A manufacturer of backpacks determines that the cost to produce 100 backpacks is $1500. The cost to produce 500 backpacks is $7000. Write a linear equation for the cost, y, of producing x backpacks.

Chapter 4

16.

Solve for x and y by substitution: x-2y=-6

y=3x-2

17. A crew rowing with the current rowed 11mi in 2 hrs. Against the current, the crew rowed 5 mi in 2 hrs. Find the rate of the current.

Mixed chapters 1-4

18. Simplify: 3x-2[x-2(x-3y)-4y]

19. Simplify: -20(36)(4)(-3)

20. Solve: y + 1.6 = 5.2.

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#### Solution Preview

1)

-12+5-(-4)-6

Break it up

-12+5=7

-(-4)-6=-2

7+-2=

5

2) Use order of operations (PEMDAS)

-2^2=-4

(-3)^2=9

-4*9*5=

-180

3) Find the common denominator to solve. In this case the lowest common multiple is 18

5/6 * 3/3=15/18

2/3 * 6/6=12/18

8/9 * 2/2=16/18

15/18-12/18-16/18=(15-12-16)/18=

-13/18

4) Line up the decimal places and solve

31.24-8.12=23.12

23.12+1.07=

24.19

5) Break it up and do it one at a time

0.8*-2.4 = -1.92

-1.92*-3.8=

7.296

6) Get x alone by adding 11 to both sides

x=7

7) Get x alone by subtracting 2/5 from both sides

x=8/15-2/5

x=8/15-6/15

x=2/15

8) Get y alone by multiplying both sides by -3/4

y=(16/27)*-3/4

y=-48/108

We ...

#### Solution Summary

This solution contains answers and work for 20 different problems relating to algebra, including solving for variables and finding slopes of lines. All work is shown in sufficient detail.