Equations Review

Absolute Value Equations

100

|x| = 9

x = {-9, 9}

200

|6c - 3| = 21

c = {-3, 4}

300

|7m| + 4 = 25

m = {-3, 3}

400

5|2n + 8| + 3 = 33

n = {-7, -1} 

500

|1/2 x + 12| = 35

x = {46, -94}

Literal Equations

100

Solve A = 1/2 bh for b

b = 2A / h

200

Solve P = 2L + 2W for L

L = (P - 2w) / 2

300

Solve s = n(a + 1) for a

a = s/n  - 1

400

Solve 1/3 (2x - y) = z for x

x = (3z + y) / 2

500

Solve -8 = 1/4 (m - n) for m

m = -32 + n

Algebraic Proportions

100

4 / 3 =  8 / x -1

x = 7

200

n - 9  / 6 =  n + 7 / 3 

n = 23

300

5 / y - 7  =  3 / y - 5

y = 2

400

3 / m - 1  =  6 / 3m + 8

m = -10

500

5 / 6 =  x - 10 / 3x + 6

x = -10

Multistep Equations

100

6y - 8 - 6 - 8y = 4

y = -9

200

-7(x + 7) = -56

x = 1

300

4(4m - 3) - (m - 5) = -52

m = -3

400

-6 - (2x + 7) = -2(x + 6) - 1 

infinite solutions

500

1/4 (5x + 16/3) - 2/3( 3/4x + 1/2) = -5

x = -8

Variables on Both Sides

100

7 - 6v = -5 - 8v

v = -6

200

5(x + 6) - 2x = 3(x + 10)

infinite solutions

300

9(k - 4) - 7k = 32 - 2(k + 8)

k = 13

400

-6(w - 4) + 8w = 2(w + 9)

no solutions

500

-4(x + 5) = 5/3 (3x - 12)

x = 0