Algebra: Solving Equations

Absolute Value Equations

100

|x| = 5

5 or -5

200

|x+7|=9

2 or -16

300

-3|y+5| = 12

no solution

400

|-8+b|-12 =2

22 or -6

500

|2x+7|+13 = 30

5 or -12

Miscellaneous

100

Use the order of operations to evaluate

5-16 + 12/2*3

7

200

One brother says of his younger brother: "Two years ago, I was three times as old as my brother was. In three years' time, I will be twice as old as my brother." How old are the each now?

Older brother is 17 and the younger brother is 7.

300

True or False

You can solve an equation with 3 or more variables.

True, they are called Literal Equations.

400

In reply to an inquiry about the animals on his farm, the farmer says: "I only ever keep sheep, goats, and horses. In fact, at the moment they are all sheep but three, all goats but four, and all horses but five." How many does he have of each animal?

The farmer has 3 sheep, 2 goats, and 1 horse.

500

Names on of Mrs. Glynn's dogs?

Clover & Cooper

Multi-Step Equations

100

10=6-2x

-2

200

15y+31=61

2

300

6=-2(7-c)

10

400

6x+3-8x=13

-5

500

5(1-2w)+8w=15

-5

Literal Equations

100

Solve for y  2y + 9 = 17 - 2x

y= 4-x    

or 

y = (8-2x)/2

200

solve for x

y=mx+b

x = (y-b)/m

300

Solve for x

2(x+7) +9y = 3y

x=-3y-7

400

Solve for F

C = (5/9)(F-32)

F=(9/5)C+32

500

Solve for h

SA = 2(pi)r²+ 2(pi)(r)(h)

h= [SA- 2(pi)r²]/[2(pi)r]

or  h= SA/[2(pi)r] -r

Variables on Both Sides

100

7k=4k+15

k=5

200

5x-2=3x+4

x=3

300

2(y+6)=3y

y=12

400

2k-5 = 3(1-2k)

k=1

500

3-5b+2b=-2-2(1-b)

b=1.4