Solving Multi-Step Equations

Variable on Both Sides

100

5h + 2 = 23 - 2h

h = 3

200

3b  - 8 = 4 - b

b = 3

300

3a + 12 = -9 + 6a

a = 7

400

4(2a + 3) =  3(a − 1)

y = -3

500

4x + 2(x+2) = 5(x-1)

x = -9

Variable on One Side

100

2x + 10 = 14

x = 2

200

5d - 10 = 40

d = 10

300

7(4 - t) = -84

t = 16

400

3x + 5 + 8x + 7 = -10

x = -2

500

-13(4 + 2a) = 208

a = -10

How Many Solutions?

100

x + 4 = x + 2

No Solution 

200

4(x + 6) = 2(2x + 12)

Infinite/All Solutions

300

2x - 4 = 3x

-4 = x

One solution

400

3x + 5 - x = 2x + 7

No Solution

500

2(4x - 8) + 2 = 8(x - 3) + 10 - x

x = 0

One Solution

Literal Equations

100

Solve for t.  d=rt

t = d/r

200

Solve for p.   q + p = d

p = d - q

300

Solve for a.  c=ars

c/rs = a

400

Solve for x.  y = mx + b

(y - b)/ m = x

500

Solve for h.   a = 1/2bh

2a/b = h

Word Problems

100

The sum of three consecutive numbers is 87.  What are those three numbers?

28, 29, 30

200

The greater of two numbers is 6 more than the smaller.  The sum of those two numbers is 34.  What are the greater and smaller number?

Smaller:  14    Greater:  20

300

Tyler has 100 apples. Tyler give his friends 3 apples each and is left with 10 apples. How friends does Tyler have?

Tyler has 30 friends

400

Serena is 5 years older than Juan.  Tina is 2 times Juan's age.  The sum of their ages is 33.  How old is Juan?

s= j + 5        t = 2j        j + 5 + 2j + j = 33

j =7

500

The width of a rectangle is 2 more than 5 times it's length.  If the perimeter is 40inches, what is the lenght AND width of the rectangle?

Length = 3 

Width = 5(3) + 2

Width = 17