Solving Equations Review

Variables on Both Sides

100

9-5k=12-(6k+7)

k=7

200

-5(x-2)=50+x+2

x=-7

300

3m-(7m+12)=2(m-3)

m=-1

400

3w-(7w+12)=2(w-3)

w=-1

500

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

n=13

No Solution & Infinite Solution

100

-7(a-3)=11-7a

21=11

No Solution

200

2x-2(4x-3)=6-6x

6=6

Infinite Solutions

300

8-3(k+2)=2-3k

2=2

Infinite Solutions

400

-3(x+5)+2x=-15-x

-15=-15

Infinite Solutions

500

-38-7y=2-7(y+6)

-38=-40

No Solution

Proportions

100

\frac{2}{9}=\frac{4}{x+8}

x=10

200

\frac{7}{x-8}=\frac{3}{x}

x=-6

300

\frac{h+9}{5}=\frac{h-1}{3}

h=16

400

\frac{6}{x-6}=\frac{3}{x-3}

x=0

500

\frac{6}{2y-5}=\frac{2}{y=7}

y=16

Absolute Value

100

\abs{x}=8

x={8,-8}

200

\abs{5c-5}=20

c={5,-5}

300

-2\abs{w+3}=-14

w={4,-10}

400

-4\abs{2w+6}=-32

w={1,-7}

500

-5\abs{4n+6}+2=-8

n={-1,-2}

Literal Equations

100

Solve for s.

p=4s

s=\frac{p}{4}

200

Solve for t.

I=prt

t=\frac{I}{pr}

300

Solve for y.

Ax+By=C

y=\frac{C-Ax}{B}

400

Solve for x.

y=\frac{1}{3}(x+1)

x=3y-1

500

Solve for p.

SA=\frac{1}{2}lp+B

p=\frac{2(SA-B)}{l}