One-Step
Solve for x:
2x + 3 > 15
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
Five friends equally split a restaurant bill that comes to $32.50. How much does each friend pay?
Each friend pays $6.50.
WORK
5x = 32.50
5x/5 = 32.50/5
x = 6.5 ~~~> $6.50
Solve for x:
x/3 > 2
x > 6
WORK
x/3 > 2
x/3 *3 > 2 *3
x = 6
Solve for x:
(x + 4) + 2x < 67
x < 21
WORK
(x + 4) + 2x < 67
x + 2x + 4 < 67
3x + 4 < 67
3x + 4 - 4 <67 - 4
3x < 63
3x/3 < 63/3
x < 21
You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. How much did you earn per hour?
You earned $9.50 per hour.
WORK
4x + 8x + 50 = 164
12x + 50 = 164
12x + 50 - 50 = 164 - 50
12x = 114
12x/12 = 114/12
x = 9.5 ~~~> $9.50
Solve for x:
5x = 20
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) > 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)
flip!
x > -7/4
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
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 and solve an equation to find the height, h, of these floors.
8h = 16 + 6h
h = 8
WORK
8h = 16 + 6h
8h - 6h = 16 + 6h - 6h
2h = 16
2h/2 = 16/2
h = 8
Solve for m:
(4/5)*m = 28
m = 35
WORK
(4/5)*m = 28
(5/4)*(4/5)*m = 28*(5/4)
m = 35
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. How many tickets did you buy?
You bought 5 tickets.
WORK
37t + 8.50t + 14.99 = 242.49
45.5t + 14.99 = 242.49
45.5t + 14.99 - 14.99 = 242.49 - 14.99
45.5t = 227.5
45.5t/45.5 = 227.5/45.5
t = 5 ~~~> 5 tickets
Solve for p:
-2.5 < -p + 7.1
p < 9.6 or 9.6 > p
WORK
-2.5 < -p + 7.1
-2.5- 7.1 < p + 7.1- 7.1
-9.6 < -p
9.6>p OR p<9.6
Solve for x:
-24 > -10x + 3
x > 2.7
WORK
-24 > -10x + 3
-24 - 3> -10x + 3 - 3
-27 > -10x
-27/(-10)>-10x/(-10)
flip!
2.7 < x
Solve for x:
3x/4 - x/3 = 10
[how do we add fractions with different denominators OR eliminate the denominators using algebra?]
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
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. What number of business cards costs the same from either printer? BONUS: What would the cost be?
Printing 100 cards would cost the same from either business.
WORK
0.10n + 15 = 0.15n + 10
0.10n - 0.10n + 15 = 0.15n - 0.10n +10
15 = 0.05n + 10
15 - 10 = 0.05n + 10 - 10
5 = 0.05n
5/0.05 = 0.05n/0.05
100 = n ~~~>100 cards
BONUS answer: It would cost $25.00 to make 100 cards from either place.
WORK
0.10n + 15 = ??
0.10(100) + 15 = 25 ~~~>$25.00
0.15n + 10 = ??
0.15(100) + 10 = 25 ~~~>$25.00