Algebra 1 - Solving Equations

One-Step Equations

100

Solve for b:

-7 = b - 3

b = -4

WORK
-7 = b - 3
-7 +3 = b - 3 +3
-4 = 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:

(4/5)*m = 28

m = 35

WORK

(4/5)*m = 28

(5/4)*(4/5)*m = 28*(5/4)

m = 35

500

Solve for p:

-2.54 = p + 7.17

p = -9.71

WORK

-2.54 = p + 7.17

-2.54- 7.17 = p + 7.17- 7.17

p = -9.71

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 a:

(1/2)a + 5 = 18

*(1/2) is "half", the same as 0.5

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

300

Solve for t:

-t + 8 = 3

t = 5

WORK

-t + 8 = 3

-t + 8 - 8= 3 - 8

-t = -5 [which is the same thing as -1t = -5]

-1t/-1=-5/-1

t = 5

400

Solve for x:

(x – 7)/3 = -12

/ mean DIVIDE so 3, is the denominator

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

[remember what fractions really look like?]

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!

Word Problems

100

Solve:

Five friends equally split a restaurant bill that comes to $32.50. WRITE the equation you can use to find how much does each friend pay?

5x = 32.50

200

Solve:

You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. WRITE THE EQUATION you can use to find how much you earned per hour?

4x + 8x + 50 = 164

300

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 an equation to find the height, h, of these floors.

8h = 16 + 6h

400

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. 

Write the equation to find how many tickets did you buy?

37t + 8.50t + 14.99 = 242.49

500

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. 

Write the equation to find what number of business cards costs the same from either printer? 

0.10n + 15 = 0.15n + 10