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Solving by Combining Like Terms
Solving by Using the Distributive Property
Variables both side
Equation Grab Bag
Word Problems
100
5h + 2 + 2h = 23
h = 3
100
2(x + 5) = 14
x = 2
100

9x - 8 = 10x - 17

x = 9

100
4x + 9 = 33
x = 6
100

WRITE AN EQUATION & SOLVE: Julie has $200 in her checking account. Each week she deposits $50.  Taylor has $650 and she withdrawals $25 each week.  How many weeks, w, will it take for both Julie and Taylor to have the same amount in their account?

200 + 50w = 650 - 25w

w = 6

200
3b + b - 8 = 4
b = 3
200
5(d - 2) = 40
d = 10
200

18x + 4 = 16x + 12

x = 4

200
x + 3x = -8
x = -2
200

Write and Equation then solve.  AT&T chargers 29.99 a month and 8 cents per text message, t.  Verizon chargers 39.99 a month plus 4 cents per text message, t.  When would both AT&T and Verizon customers have the same cost?

29.99 + .04t = 39.99 + .04t

t = 250

300
3a + 12 - 6a = -9
a = 7
300
7(4 - t) = -84
t = 16
300

3(x+6) = 2x + 24

x = 6

300
4(y - 2) + y = -13
y = -1
300

Write an equation and solve. 

Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil? 

120 + 10m = 150 + 4m

m = 5

400
-6 = -3y + 4 + 5y
y = -5
400
-2(x - 9) = -24
x = 21
400

4(x-2) - 16 = 3x -32

x = 8

400
-6(m + 1) + 18 = 24
m = -2
400

You are looking for an apartment. There are two final choices. Apartment A has a $1000 security deposit and costs $1200 each month. Apartment B has a $1500 security deposit and costs $1175 each month. How many months, m, will it take for the costs to be the same?

1,000 + 1200m = 1500 + 1175m

m = 20

500
78 = 3c + 12 - c + 4
c = 31
500
-13(4 + 2a) = 208
a = -10
500

6(x+2) - 8 = 4(x+4) + 4

x = 8

500
7k - 8 + 2(k + 12) = 52
k = 4
500

Lenny makes $55,000 and is getting annual raises of $2,500. Karl makes $62000, with annual raises of $2,000. How many years, y, will it take for Lenny and Karl to make the same salary?

55,000 + 2,500y = 62,000 + 2,000y