Writing and Graphing Inequalities
Write the sentence as an inequality:
The quotient of twice a number y and 3 is at most 6.
2y ÷ 3 ≤ 6
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Solve the inequality. Graph the solution.
-21 ≤ -7x
x ≤ 3
See Graph. Closed circle arrow to the left.
Solve the inequality. Graph the solution.
a. 6 < -5t - 4
b. m ÷ 4 + 2 < 3
See Graphs.
a. t < -2
b. m < 4
Write the sentence as an inequality. Graph the inequality.
A number d is at most two and greater than -2.
-2 < d ≤ 2
See Graph.
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Solve the inequality.
|2x - 9| < -8
No solution.
Tell whether the value g = -2 is a solution of the inequality.
12 < 18 ÷ (3g) + 12
No
Write the sentence as an inequality. Then solve and graph.
"The sum of a number x and 7 is at most 15."
x + 7 ≤ 15
x ≤ 8
See Graph. Closed Circle, Arrow to the left.
Solve.
10h - 3h + 6 ≥ 11 + 7h
No solution.
Solve the inequality. Graph the solution.
-2 ≥ 10 - 3g ≥ -8
4 ≤ g ≤ 6
See Graph.
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Solve the inequality. Graph the solution.
|5x - 1| - 7 ≥ 2
x ≤ -1.6 or x ≥ 2
See Graph.
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Graph the inequality.
n < |-4|
See solution.
The school baseball record for no-hitter innings is 112 in a season. This year's team currently has 87 no-hitter innings. What are the possible numbers of additional no-hitter innings the team can achieve to match or break the school record in a season?
x ≥ 25 innings
DAILY DOUBLE: EARN DOUBLE THE POINTS!
Solve.
-4(2x - 6) ≤ 8(3 - x)
All Reals
Solve the inequality. Graph the solution.
15 < -v - 8 or 3v + 4 ≥ 10
v < -23 or v ≥ 2
See Graph.
Solve the inequality.
|y - 2| + 11 > 0
All Reals
The winning swim team earned 245 points. The other teams earned at least 72 points less.
a. Write an inequality that represents the points that the other teams earned.
b. Was one of the teams able to earn 180 points?
a. x ≤ 173 points
b. no
Write and solve an inequality to find the possible values. The perimeter of a triangle is less than 37.8 meters. You know the lengths of two sides:
11.8 m and 12.5 m
What are the possible values of the third side, x?
11.8 + 12.5 + x < 37.8
x < 13.5 m
Write and solve an inequality.
The area of a rectangle is more than 47 square meters. Find the possible values of n if the width of the rectangle is 2 meters and the length of the rectangle is (3n - 5) meters.
n > 9.5 meters
Solve the inequality. Graph the solution.
-6 < 1/3(6y + 12) < 14
-5 < y < 5
See Graph.
Solve the inequality. Graph the solution.
3|2a + 8| - 11 ≤ -5
-5 ≤ a ≤ -3
See Graph.
A rectangle has a length of x units and a width of 16 units. Write an inequality that represents the possible values of x that would make the area of the rectangle at least 112 square units.
x ≥ 7 units
You are scanning tickets at a concert. You have determined that you are scanning 16 tickets each minute. How many minutes, m, will it take for you to scan at least 136 tickets? Write and solve an inequality.
16m ≥ 136
x ≥ 8.5 minutes
Your friend has $60 and plans to save $25 each month. Write and solve an inequality that describes the number of months your friend needs to save to buy a new TV that cost $680.
Inequality: 60 + 25m ≥ 680
Answer: m ≥ 24.8 months, thus your friend needs to save for greater than or equal to 25 months.
To get a discounted ticket to a ball game, you must be younger than five years old or at least 60 years old. Write an inequality that represents the acceptable ages for a discounted ticket.
x < 5 or x ≥ 60
Solve the inequality. Graph the solution.
2|1 - 3h| + 9 < 29
h < -11/3 and h > -3
See Graph.