Solving Inequalities
Graphs
Compound Inequalities
Absolute Value Inequalities
Challenge
100
Solve n + 8 > 6. Describe your solution in words.
n > -2 All values of n greater than -2 are solutions.
100
Describe the difference between the meaning of an open circle and a closed circle on a number line graph.
An open circle means the number it is on is a boundary, but is not included as part of the solution. A closed circle means that number is included as part of the solution.
100
Re-write -3 < x < 5 as two inequalities.
-3 < x and x < 5
100
What is the first step in solving any absolute value inequality?
Get that absolute value part by itself (get rid of any numbers on the outside of the absolute value sign).
100
To join the school's cross country team, runners must be able to run at least 3500 yards without stopping. Write an inequality that represent this scenario.
y is greater than (>) or equal to 3500
200
Solve -8m > -88
m < 11
200
Graph n < 7
Open circle on 7, shaded to the left.
200
Describe the difference of a solution to an "and" inequality and an "or" inequality.
With an "and" inequality a number that is a solution must work for both of the inequalities involved in the problem; with an "or" inequality the number has to work for just one to be part of the solution.
200
Solve |3x| < 15
-5 < x < 5
200
In order to go on a class trip the group must raise at least $3000. So far they have raised $1250 dollars. Write and solve an inequality representing the situation and how much more they must earn to be eligible for the class trip.
m > or = $1750
300
Solve 2h - 9 + 8h > 21
h > 30
300
Graph x < 4 or x > 6
Open circle on 4 shaded to the left, open circle on 6 shaded to the right.
300
Solve -3x > 12 or 2x + 5 > 17
x < -4 or x > 6
300
Solve 2 + | x - 5 | > 9
x > 12 or x < -2
300
Tom plans to sell t-shirts at his town's celebration days this summer to earn money for a trip. The city charges him $150 to reserve a tent to sell his shirts. It will cost him $4 to make each shirt and he will sell them for $10. Write and solve an inequality showing how many shirts will he need to sell in order to make a profit.
t > 25, so he must sell 26 or more t-shirts to make a profit.
400
Solve 6(z - 4) > 3(2z + 12)
No solution. When you simplify you get 6z - 24 > 6z + 36, or -24 > 36. -24 is never greater than 36, so there is no solution.
400
Graph the solution to -8 < x - 12 < 2
Open circles on 4 and 14, shaded in between the two numbers.
400
Solve -3 < 2m + 1 < 11
-2< m < 5
400
Solve -2|x + 4| > -12
-10 < x < 2
400
Jim's music class is putting on a concert. Tickets cost $3.50 each and he wants to buy as many tickets as he can afford. He has $20 to spend. Write and solve an inequality to show how many tickets he can buy.
t < or = 5.7 so he could buy at most 5 tickets.
500
Solve 9(t - 3) - 12t > 2t + 13
t < -8
500
Draw a graph that represents the solution n = all numbers except 3.
A number line with an open circle at 3 and arrows shading in both directions.
500
Solve -5x > 10 and 2x - 7 > 5
x < -2 and x > 6 but since x cannot be less than -2 and bigger than 6 at the same time, x does not exist, therefore there is no solution.
500
Solve 10 |3x - 27| + 14 < 0
No Solution
500
Kristen wants to buy a gym membership to work out. Gym A has a joining fee of $100 and charges $25 per month for membership. Gym D charges a monthly rate of $45. Write and solve an inequality showing how many months Kristen would need to be a member of a gym for it to cheaper for her to go with Gym A.
m > 5, so starting on the 6th month it would be cheaper to be a member of Gym A.
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