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

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

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!

Vocabulary

100

This consists of two expressions separated by an equal sign.

Equation

200

A number dependent on the variable and it is multiplying by the variable.

Coefficient

300

An unknown value in an expression or equation.

Variable

400

An independent value or number that never changes in an equation.

Constant

500

A grouping together of one or more factors (variables and/or numbers) that can be combined.

Like terms