Solving Multi-Step Equations

Solving by Combining Like Terms

100

5h + 2 + 2h = 23

h = 3

200

3b + b - 8 = 4

b = 3

300

3a + 12 - 6a = -9

a = 7

400

-6 = -3y + 4 + 5y

y = -5

500

78 = 3c + 12 - c + 4

c = 31

Absolute Value and Literal Equations

100

|m + 6| -14 if m = 4

-4

200

23 - |13 - 4x|  if x = 2

18

300

|f + 5| = 17

12 and -22

400

3x - 2y = 10  solve for x

(10 +2y)/3

500

v = 1/3xrh   solve for r

3v/xh

Variables on Both Sides

100

3w + 2 = 7w

1/2

200

5a + 2 = 6 - 7a

1/3

300

1/2x +1 = 1/4x -6

-28

400

8x - 10 = 3(6 - 2x)

2

500

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

No solution

Equation Grab Bag

100

4x + 9 = 33

x = 6

200

x + 3x = -8

x = -2

300

4(y - 2) + y = -13

y = -1

400

-6(m + 1) + 18 = 24

m = -2

500

7k - 8 + 2(k + 12) = 52

k = 4

Word Problems

100

Seventeen is thirteen subtracted from six times a number.  What is the number?

6x - 13 = 17   which is 5

200

Fourteen less than three fourths of a number is negative eight.  Find the number.

3/4n - 14 = -8  which is 8

300

Find three consecutive even integers with the sum of -84

n = n +2 = n + 4 =

-30, -28, -26

400

Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?

r - cost of a bag of raisins 17r + 2.97 = 34.76 r = 1.87 Each bag of raisins cost $1.87

500

When you count by ones fron many integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?

n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.