Inequalities
Solve:
3(x + 12) > 45
Graph the solution set on the number line.
x > 3
How many solutions does this problem have?
4(2x + 1) = 5(x + 2) + 3
5t - 4= t - 8
t=-1
4(−x + 4) = 12
x = 1
Your sister bought pencils at $0.39 each and a notebook at $1.19. The total cost was $3.92. How many pencils did she buy?
0.39p + 1.19 = 3.92 and p = 7 pencils
Solve and graph your answer:
5(x + 6.25) > 51
X > 3.95
How many solutions does this problem have?
6(x – 6) = 2(6 + 3x)
No solutions
7 + 3h = -1 -5h
h= -1
37 = −3 + 5(y + 6)
y = 2
Eight less than twice a number is equal to sixteen less than three times the number. What is the number?
2x - 8 = 3x -16 and x = 8
Solve –2x + 9 ≥ –5.
Graph the solution set on the number line.
x ≤ 7
How many solutions does this problem have?
3(4x - 4) = 4(3x - 3)
Infinite solutions
Solve
–2.7x + 3.5 = 1.3x + 11.5.
x = -2
−13 = 5(1 + 4m) − 2m
m = -1
Trey has a 50 gallon water tank. He fills the tank with a garden hose at a rate of 4.4 gallons per minute. There are 6 gallons of water in the tank. What is the maximum amount of time Trey can add water without causing the tank to overflow?
50 ≥ 6 + 4.4x
10 ≥ x
Solve
-2x - 9 ≤ 5.
Graph the solution set on the number line.
b ≥ -7
In the equation below, what values will result in no solution?
4x – 2(3x + 7) = ______x – ______
-2x - (any number besides 14)
Solve –2(4x + 6) + 4 = 2(5x – 9) – 8x
x = 1
−8(−8w − 6) = −6w − 22
w = -1
Two companies offer Jane a sales position. Company A pays $3,000 each month plus $250 per car sold. Company B pays $2,500 each month plus $350 per car sold.
Write an equation could be used to determine the number of cars sold in a month, x, that would result in the same total income from each company?
3000 + 250x = 2500 +350x
x = 5
Solve
(3/2)(x) < 6 - 12x.
Graph the solution set on the number line.
x< 4/9
In the equation below, what values will result in infinite solutions?
5x – 2(3x + 6) = ______x – ______
-1x - 12
Solve
0.1(x + 8) - 0.5x = 0.2(2x - 6) + 5.2.
x = -4
5(2a+6)=−4(−5−2a)+3a
a = 10
Cailen needs at least $150 to buy a video game system. She earns $15 for each lawn she mows and has $30 in savings. Write and solve an inequality to determine how many lawns Cailen must mow to buy the video game system.
150 ≤ 15x + 30
8 ≤ x