Solving Inequalities Part 1
Solve
x+3>9
x>6
Solve:
4r+8<12r
r>1
Write a linear inequality:
A number decreased by 7 is at most 13.
x-7≤13
Write a linear inequality and solve it:
Jesse wants to buy more glass ducks. Each glass duck costs 12.50 but Jesse only has $150 total.
12.50x≤150
What does this symbol called, ">" ?
greater than
or more than
Solve
(x/5)– 11 ≥ -14
x≥-15
Solve:
3x+7>3x
No solution
Write a linear inequality:
A number plus 6 is greater than 1.
x+6>1
Write a linear inequality and solve it:
Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?
5.50x≥5225
Graph the Inequality
8d < 24
d<3
Open circle at 3 and arrow going to the left.
Solve
7 < 4q - 9
q>4
Solve:
4x-5>24x+5
x<-1/2
Write a linear inequality:
A sum of a number and 14 is at least 28
x+14≥28
Write a linear inequality and solve it:
Adrian works in New York City and makes $42 per hour. She works in an office and must get her suit dry cleaned everyday for $75. She wants to make at least $260 a day.
42x-75≥260
Graph the Inequality
-15 ≥ -3x -45
-10≤x
Dot at -10 and the arrow is going to the right
Solve
21 ≤ 3 + 9x
x≥2
Solve:
-3x+6<18-x
x>-6
Write a linear inequality:
the product of a number and 4 is decreased by 5 is less than 32
4x-5<32
Write a linear inequality:
Pedro is ordering a flower arrangement with roses and carnations. He doesn't want to spend more than $46 on the arrangement. Roses cost $5 each and carnations cost $1 each.
x= the number of roses
y= the number of carnations
5x+y≤46
What does "inverse operation" mean?
eg. what is the inverse operation of 3x/4?
x divided by 3/4
or times 4/3
Solve
(2x-3)/-5<3
x>-6
Solve:
2x+6x+16<12x-8
x>6
Write a linear inequality:
Twice a number is more than the sum of that number and 8.
2x>x+8
Write a linear inequality:
The manager of an electronics store projects that the store should achieve more than $11,000 in revenue from TVs and DVD players every day in order to remain profitable. Its DVD players sell for $63, and TVs sell for $690.
x= the number of DVD players sold
y= the number of TVs sold
11,000<63x+690y
Graph the Inequality
(x/3)+2≥9
x≥21
Dot at 21 and arrow going to the right.