Algebra 1 - Solving Equations

Two-Step Equations

100

Solve for x:

2x + 3 = 15

x = 6

WORK

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

(2x)/2 = 12/2

x = 6

200

Solve for a:

-(1/2)a - 5 = 18

a = 26

WORK

-(1/2)a - 5 = 18

(1/2)a - 5 + 5 = 18 + 5

-(1/2)a = 23

(-2)*(-1/2)a = 23*(-2)

a = -46

300

Solve for t:

-14t + 8 = 50

t = -3

WORK

-14t + 8 = 50

-14t + 8 - 8 = 50 - 8

-14t = 42

-14t/(-14) = 42/(-14)

t = -3

400

Solve for x:

(x – 7)/3 = -12

x = -29

WORK

(x – 7)/3 = -12

3*((x – 7)/3)= -12*3

x – 7 = -36

x – 7 + 7= -36 + 7

x = -29

500

Solve for x:

-24 = -10x + 3

x = 2.7

WORK

-24 = -10x + 3

-24 - 3= -10x + 3 - 3

-27 = -10x

-27/(-10)=-10x/(-10)

2.7 = x

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:

-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

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:

3x/4 - x/3 = 10

x = 24

WORK

3x/4 - x/3 = 10

9x/12 - 4x/12 = 10 [write fractions/common denominator]

5x/12 = 10

12*(5x/12) = 10*12

5x/5 = 120/5

x = 24

Variables on Both Sides

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:

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

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!

Distributive Property

100

Solve for d:

(1/3)(d + 9) = -12

d = -5

WORK

(1/3)(d + 9) = -12

(1/3)d + 3 = -12 [Distributive Property]

(1/3)d + 3 - 3 = -12 - 3

(1/3)*(1/3)d = -15*(1/3)

d = -5

200

Solve for d:

7(d - 5) + 12 = 5

d = 4

300

Solve for x:

-8(2x + 7) = -4(x + 20)

x = 2

WORK

-8(2x + 7) = -4(x + 20)

-16x - 56 = -4x - 80

-16x - 56 + 16x = -4x - 80 + 16x

-56 = 12x - 80

-56 + 80 = 12x - 80 + 80

24 = 12x

24/12 = 12x/12

x = 2

400

Solve for n:

15 = 4.3n - 2.1(n - 4)

n = 3

WORK

15 = 4.3n - 2.1(n - 4)

15 = 4.3n - 2.1m + 8.4 [Distributive Property]

15 = 2.2n + 8.4

15 - 8.4 = 2.2n + 8.4 - 8.4

6.6 = 2.2n

6.6/2.2 = 2.2n/2.2

n = 3

500

Solve for z:

0.25(8z - 4) = z + 8 - 2z

z = 3

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