Algebra 1 - Solving Equations

One-Step Equations

100

Solve for b: you need to show your work

7 = b - 3

b = 10

WORK

7 = b - 3

7 +3 = b -3 +3

10 = b

200

Solve for x:

x÷3 = 2

x = 6

WORK

x/3 = 2

x/3 *3 = 2 *3

x = 6

300

Solve for x:

5x = 20

(When you see it written 5x that means the same thing as 5*x)

x = 4

WORK

5x = 20

5x÷5 = 20÷5

x = 4

400

Solve for m:

(m-7)÷2 = 28

m = 63

WORK

(m-7)÷2 = 28

(m-7)÷2 x 2 = 28 x2

m-7 =56

m-7+7 = 56 +7

500

Solve for p:

7.17 = p + 2.54

p = 4.63

WORK

7.17 = p + 2.54

7.17-2.54=p

4.63=p

Two-Step Equations

100

Solve for x:

2x + 3 = 15

(When you see it written 2x that means the same thing as 2*x)

x = 6

WORK

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

(2x)/2 = 12/2

x = 6

200

Solve for X

24 = 10x + 3

WORK

24 = 10x + 3

24 - 3= 10x + 3 - 3

21 = 10x

2.1=x

300

Solve for t:

3 + t = 8

t = 5

WORK

3 + t = 8

t = 8-3

400

Solve for x:

(x – 7)÷3 = 12

x = 43

500

Solve for a:

(1/2)a + 5 = 18

Hint: anything beside brackets means multiplication

a = 26

WORK

(1/2)a + 5 = 18

(1/2)a + 5 - 5 = 18 - 5

(1/2)a = 13

2*(1/2)a = 13*2

a = 26

Multi-Step Equations

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

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

300

Solve for x:

5x - 10 = 26

x = 7.2

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

500

Solve for x:

9x + 12 = 84

x = 8

The balance scale - what you take off one side...

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

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

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

400

Solve for x:

6x + 2 = 5x + 7 

x = 5

500

Solve for x:

3x+4=2x+5

x = 1

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