Solving Equations
3x+7 = -8
x=-5
-3 > x - 11
8 > x or x < 8
If 2 times a number is increased by 35, the result is 21 less than 9 times the number.
2x + 35 = 9x - 21
x=8
-4 < 2x + 8 < 18
-6 < x < 5
The temperature x must be more than 10 degrees and at most 25 degrees. Write the compound inequality.
10 < x < 25
9x - 4 = 2x + 3
x = 1
4 < -2(x + 3)
-5 > x or x < -5
If 5 times a number is increased by 15, the result is 12 less than 8 times the number.
5x + 15 = 8x - 12
x=9
-13 > x + 2 or 5x > -15
x < -15 or x >-3
Water is not a liquid if its temperature is above 100 degrees or below 0 degrees
x > 100 or x < 0
2(4x + 6) = 2/3(12x + 18)
All real numbers
5 - 8(1 + 6x) < -3(1 - x)
x > 0
The perimeter of a triangle is 120 inches. The second side is 8 inches longer than 3 times the first side, and the third side is 2 inches shorter than twice the first side. How long is each side?
side 1 = 19
side 2 = 65
side 3 = 36
15 < -v - 8 or 3v + 4 > 10
v < -23 or v > 2
Penny plans to spend between $20 and $25 on dinner. If she buys two pork chops at $7.50 each, how many potatoes can she buy while staying in her price range if the potatoes cost $0.50 each.
20 < 15 + 0.50x < 25
10 < x < 20
2x - 5(x - 3) = 2(x - 10)
x = 7
6(x - 1) > 2(3x - 5)
All real numbers
You are saving for a new phone. You start with $200 and plan to save $50 every month. Your friend starts with $100 and saves $75 each month. After how many months will you and your friend have saved the same amount?
4 months
-6 < 1/3(6x + 12) < 14
-5 < x < 5
A box of cereal must weigh more than 629.4g and less than 630.6g to pass inspection. The box in which the cereal is packaged weighs 5.5g. What are the possible weights for the cereal?
623.9 < x < 625.1
6(3x + 1) - 30 = 3(2x - 4)
x = 1
6(1/3x + 4) > 2(x+12)
No Solution
Find a number such that 7 more than 1/4 of the number is 5 less than 2/5 of the number.
80
-2x < -8 and -2x + 3 <1
x>4
Carmen works in a sporting goods store. Her goal is to sell between $500 and $600 worth of sporting equipment every week. So far this week, she has sold $395 worth of equipment. During the rest of the week, what dollar amount must Carmen sell in order to reach her goal?
105 < x < 205