Algebra 1 - Solving Equations

Absolute Value Equations

Write & Solve the Equation

Multi-Step Equations

Variables on Both Sides

Word Problems

100

Solve for b:

-7 = lbl

No Solution

100

The sum of a number and 5 is 12. Find the number.

x+5=12

x=7

100

Solve for m:

5 = 5m - 23 + 2m

m =4

WORK

5 = 5m - 23 + 2m

5 = 5m + 2m - 23

5 = 7m - 23

5 + 23 = 7m - 23 + 23

28 = 7m

28/7 = 7m/7

4 = m

100

Solve for b:

3b - 4 = b + 2

b = 3

WORK
3b - 4 = b + 2
3b - 4 + 4 = b + 2 + 4
3b = b + 6
3b - b = b - b + 6
2b = 6
2b/2 = 6/2
b = 3

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 for x:

l ^x/₃ l = 2

x = 6

x = -6

200

3 less than a number is -5

x - 3 = -5

x = -2

200

Solve for x:

(x + 4) + 2x = 67

x = 21

WORK

(x + 4) + 2x = 67

x + 2x + 4 = 67 [addition is commutative]

3x + 4 = 67

3x + 4 - 4= 67 - 4

3x = 63

3x/3 = 63/3

x = 21

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

200

Solve:

You work for 4 hours on Saturday and 8 hours on Sunday. Plus 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 for x:

l 5xl +5 = 20

x = 3

x = -3

300

The quotient of a number and 6 is -51.

^x/₆ = -51

x = -306

300

Solve for x:

-8(2x - 1) = 36

x = -7/4

WORK

-8(2x - 1) = 36

-16x + 8 = 36 [Distributive Property]

-16x + 8 - 8 = 36 - 8

-16x = 28

-16x/(-16) = 28/(-16)

x = -7/4

300

Solve for p:

1.5p = 1.25p + 8

p = 32

WORK
1.5p = 1.25p + 8
1.5p - 1.25p = 1.25p - 1/25p + 8
0.25p/0.25 = 8/0.25
p = 32

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 for m:

2 l m+1 l - 5 = 3

m = 3

m = -5

400

The difference of twice a number and 7 is -103.

2x - 6 = -103

x = -48.5

400

Solve for x:

3.5 - 0.02x = 1.24

x = 113

WORK

3.5 - 0.02x = 1.24

100*(3.5 - 0.02x) = 1.24*100

350 - 2x = 124 [Distributive Property]

350 - 350 - 2x = 124 - 350

-2x/(-2) = -226/(-2)

x = 113

400

Solve for x:

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

x = 5

WORK
2(5x - 1) = 3(x + 11)
10x - 2 = 3x + 33 [Distribute]
10x - 3x - 2 = 3x - 3x + 33
7x - 2 + 2 = 33 + 2
7x/7 = 35/7
x = 5

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 for p:

-2 l 2p + 10 l + 4 = -20

p = 1

p = -11

500

Two times the quantity of the sum of a number and 3 is 11.

2(x+3)=11

x=2.5

500

Solve for x:

3x + x/3 = -10

x = -3

500

Solve for x:

9m - 4 = -3m + 5 + 12m

NO SOLUTION

-4 = 5

WORK

9m - 4 = -3m + 5 + 12m

9m - 4 = -3m + 12m + 5

9m -9m - 4 = 9m -9m + 5

-4 = 5 <~~~NO! So, No Solution!

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