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One-Step Equations
Two-Step Equations
Multi-Step Equations
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Literal Equations
100
Solve for b:

-7 = b - 3
b = -4

WORK
-7 = b - 3
-7 +3 = b - 3 +3
-4 = b
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 h in the following literal equation: 

 A=b⋅h


 


Answer:

h = A/b


200
Solve for x:

x/3 = 2
x = 6

WORK
x/3 = 2
x/3 *3 = 2 *3
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
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:

4(x+y)=P


Answer:

x=(4/P)−y


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
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 r in the following equation:

V=πr2h

Answer:

r = Radical(V/πh)

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
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

The formula Ax + By = C represents the equation of a line in standard form. Which expression represents y in terms of A, B, C, and x?


y = (C - Ax) / B

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
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

A formula for determining the finite sum, S, of an arithmetic sequence of numbers is

S = n/2 (a + b), where n is the number of terms, a is the first term, and b is the last term. Express b in terms of a, S, and n.



b = (2S/n) - a