Absolute Value
Two-Step Equations
Multi-Step Equations
Variables on Both Sides
Literal Equations
100

Solve for x:

|x|=6

{-6,6}

WORK

x=-6

x=6

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
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 for x:


z=m-x

m-z=x


WORK

z=m-x (subtract m)

z-m=-x (divide by -1)

m-z+x

200

Solve for x:

|x-4|=5

{-1,9}

WORK

x-4=-5 (add 4)

x=-1

and

x-4=5 (add 4)

x=9

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
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 for x:

g=6x

x=g/6

WORK

g=6x (divide by 6)

x=g/6

300

Solve for x:


|2x+5|=25

{-15,10}

WORK

2x+5=-25 (subtract 5)

2x=-30 (divide by 2)

x=-15

and

2x+5=25 (subtract 5)

2x=20 (divide by 2)

x=10 

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
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 for a:

am=n+p

a= (n+p)/m

WORK

am=n+p (divide by m)

a=(n+p)/m

400

Solve for x:

2|x-4|+3=11

{0,8}

WORK

First, isolate |x-4| 

2|x-4|+3=11 (subtract 3)

2|x-4|=8 (divide by 2)

|x-4|=4

Second, set the expression in the absolute value equal to positive and negative 4

x-4=-4 (add 4)

x=0

and

x-4=4 (add 4)

x=8

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
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 for x:

g=x-c+y


x=g+c-y

WORK

g=x-c+y (add c)

g+c=x+y (subtract y)

g+c-y=x 

500

Solve for x:

2|x+1|+5=1

no solution!

WORK

First, isolate |x+1|

2|x+1|+5=1 (subtract 5)

2|x+1|=-4 (divide by 2)

|x+1|=-2 

Since the absolute value can never equal a negative number, in this case -2, the answer is no solution. 

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
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
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 for x:

u=kx+yx


x=u/(k+y)

WORK

u=kx+yx (factor out x from both terms) 

u=(k+y)x (divide by factor (k+y))

u/(k+y)=x

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