One-Step Equations
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
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
Solve:
Five friends equally split a restaurant bill that comes to $35.00. How much does each friend pay?
Each friend pays $7.00.
WORK
5x = 35.00
5x/5 = 35.00/5
x = 7.00 ~~~> $7.00
Solve for a:
a/2 + 5 = 18
a = 26
WORK
a/2 + 5 = 18
a/2 + 5 - 5 = 18 - 5
a/2 = 13
a/2 x 2 = 13 x 2
a = 26
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
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
Solve:
You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $194.00 total. How much did you earn per hour?
You earned $12.00 per hour.
WORK
4x + 8x + 50 = 194
12x + 50 = 194
12x + 50 - 50 = 194 - 50
12x = 144
12x/12 = 144/12
x = 12 ~~~> $12.00
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
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
Solve for x:
8(2x + 1) = 40
x = 2
WORK
8(2x + 1) = 40
16x + 8 = 40
16x + 8 - 8 = 40 - 8
16x/16 = 32/16
x = 2
Solve for p:
3p = 2p + 8
p = 8
WORK
3p = 2p + 8
3p - 2p = 2p + 8 - 2p
p = 8
Solve:
Two buildings have the same total height. One building has 8 floors with height, h. The other building has a ground floor of 4 metres and 6 other floors with height, h. Write and solve an equation to find the height, h, of these floors.
8h = 4 + 6h
h = 2 metres
WORK
8h = 4 + 6h
8h - 6h = 4 + 6h - 6h
2h = 4
2h/2 = 4/2
h = 2
Solve for m:
m/4 = 7
m = 28
WORK
m/4 = 7
m/4 x 4 = 7 x 4
m = 28
Solve for x:
(x – 7)/3 = 12
x = 43
WORK
(x – 7)/3 = 12
3*((x – 7)/3)= 12*3
x – 7 = 36
x – 7 + 7= 36 + 7
x = 43
Solve for x:
7x + 3 = 36
x = 4
WORK
7x + 3 = 31
7x + 3 - 3 = 31 - 3
7x/7 = 28/7
x = 4
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
Solve
Online concert tickets cost $30 each, plus a service charge of $5.00 per ticket. The Web site also charges a transaction fee of $15.00 for the purchase. You paid $155.00. How many tickets did you buy?
You bought 4 tickets.
WORK
30t + 5.00t + 15.00 = 155.00
35.00t + 15.00 = 155.00
35.00t + 15.00 - 15.00 = 155.00 - 15.00
35.00t = 140.00
35.00t/35.00 = 140.00/35.00
t = 4 ~~~> 4 tickets
Solve for p:
7.57 = p + 2.14
p = 5.43
WORK
7.57 = p + 2.14
7.57 - 2.14 = p + 2.14 - 2.14
5. 43 = p
Solve for x:
-27 = -10x + 3
x = 3
WORK
-27 = -10x + 3
-27 - 3= -10x + 3 - 3
-30 = -10x
-30/(-10)=-10x/(-10)
3 = x
Solve for x:
2x + 4x = 36
x = 6
WORK
2x + 4x = 36
6x = 36
6x/6 = 36/6
x = 6
Solve for x:
9m - 4 = -3m + 5 + 12y
m - 4 = y - 5
WORK
9m - 4 = -3m + 5 + 12y
9m - 4 + 3m= 5 + 12m
12m - 4 = 12y+ 5
m - 4 = y - 5
Solve
Pristine Printing will print birthday cards for $2 each plus a setup charge of $15. The Printing Place offers birthday cards for $3 each with a setup charge of $10. If I wanted 10 birthday cards for my business, which company would save me the most money?
BONUS: How much would I save?
Using Pristine Printing offers the best deal.
WORK
(2 x 10) + 15 = (3 x 10) + 10
20 + 15 = 30 +10
35 = 40
BONUS answer: You would save $5 using Pristine Printing