Algebra 1 - Solving Equations

Expressions with Absolute Value

100

Evaluate lm + 6l - 14 if m=4

-4

200

Evaluate 23- l3-4xl if x=2

18

300

Evaluate lf + gl - h 

if f=3, g= -4, and h = 5

-4

400

Evaluate 4a - l3b + 2c l 

if a= -2, b= -3, c= 2

-13

500

Evaluate -4 lc - 3l + 2 l z-a l

if a= -2, c= 2, z= -4.2

.4

Absolute Value Equations

100

lv - 2l = -5

No Solution

200

l 8w + 5 l =21

-3.25, 2

300

l 3/4a - 3 l = 9

-8, 16

400

4 -3lql = 10

No solution

500

4/lpl + 12 = 14

-2, 2

Variables on Both Sides

100

2(5x - 1) = 3(x + 11)

x =5

200

-5(3-q) + 4 = 5q - 11

infinite

300

5[2p - 4(p + 5)] = 25

-12.5

400

2(4r +6) = 2/3(12r + 18)

Infinite

500

2m/5 = 1/3(2m - 12)

15

Multi-step Equations

100

5x/9 -11 = -51

-72

200

Solve for x:

5x + 2 = 2x + 14

x = 4

WORK
5x + 2 = 2x + 14
5x + 2 - 2 2x + 14- 2
5x = 2x + 12
5x - 2x = 2x - 2x + 12
3x = 12
3x/3 = 12/3
x = 4

300

(5v-4)/10 = 4/5

2 2/5

400

12 - 4/5(x + 15) =4

-5

500

(b-4)/6 = b/2

-2

Word Problems

100

Solve:

Five friends equally split a restaurant bill that comes to $32.50. How much does each friend pay?

Each friend pays $6.50.

WORK
5x = 32.50
5x/5 = 32.50/5
x = 6.5 ~~~> $6.50

200

Solve:

You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. How much did you earn per hour?

You earned $9.50 per hour.

WORK
4x + 8x + 50 = 164
12x + 50 = 164
12x + 50 - 50 = 164 - 50
12x = 114
12x/12 = 114/12
x = 9.5 ~~~> $9.50

300

Solve:

Two buildings have the same total height. One building has 8 floors with height, h. The other building has a ground floor of 16ft and 6 other floors with height, h. Write and solve an equation to find the height, h, of these floors.

8h = 16 + 6h
h = 8

WORK
8h = 16 + 6h
8h - 6h = 16 + 6h - 6h
2h = 16
2h/2 = 16/2
h = 8

400

Solve

Online concert tickets cost $37 each, plus a service charge of $8.50 per ticket. The Web site also charges a transaction fee of $14.99 for the purchase. You paid $242.49. How many tickets did you buy?

You bought 5 tickets.

WORK
37t + 8.50t + 14.99 = 242.49
45.5t + 14.99 = 242.49
45.5t + 14.99 - 14.99 = 242.49 - 14.99
45.5t = 227.5
45.5t/45.5 = 227.5/45.5
t = 5 ~~~> 5 tickets

500

Solve

Pristine Printing will print business cards for $0.10 each plus a setup charge of $15. The Printing Place offers business cards for $0.15 each with a setup charge of $10. What number of business cards costs the same from either printer? BONUS: What would the cost be?

Printing 100 cards would cost the same from either business.

WORK
0.10n + 15 = 0.15n + 10
0.10n - 0.10n + 15 = 0.15n - 0.10n +10
15 = 0.05n + 10
15 - 10 = 0.05n + 10 - 10
5 = 0.05n
5/0.05 = 0.05n/0.05
100 = n ~~~>100 cards

BONUS answer: It would cost $25.00 to make 100 cards from either place.

WORK
0.10n + 15 = ??
0.10(100) + 15 = 25 ~~~>$25.00

0.15n + 10 = ??
0.15(100) + 10 = 25 ~~~>$25.00