Intro to Inequalities
How many different inequality signs are there?
<, \le, >, \ge (4)
x + 8 \le 19
x \le 11
4x + 9 < 33
x < 6
Liam earns $10 per hour mowing lawns. He wants to save at least $50 to buy a video game. Write an inequality to find the minimum number of hours, h, Liam needs to work.
10h \ge 50
-1.2 + 3.45
2.25
What are the only two times when we flip the sign when solving an inequality?
(1) When our variable starts on right side, (2) When we divide/multiply by a negative number to isolate our variable
-5x > 35
x < -7
-3w - 11 \ge 16
w \le -9
A submarine at an elevation of -120 feet descends at a rate of 20 feet per minute. Write an inequality to determine the time in minutes, t, when the submarine's elevation will be below -260 feet.
-120 - 20t < -260
-4.5 \times (-0.8)
3.6
Graph x > -5
Answers may vary
m - 4.6 \ge 3.8
m \ge 8.4
0.3(p - 4.0) > 1.8
p > 10
A warehouse holds 460 boxes. They ship out 65 boxes each week. After how many weeks will the warehouse have less than 100 boxes remaining? Write and solve an inequality that can be used to determine how many weeks it will take for the warehouse to have less than 100 boxes.
x > 5.54 weeks
-\frac{3}{5} + \frac{7}{10}
\frac{1}{10}
Name four math clue words for \le
maximum, at most, less than or equal to, no greater than, no more than
-\frac{3}{4}y < \frac{9}{10}
y > - \frac{6}{5}
-\frac{2}{3}(n + \frac{1}{2}\) \le \frac{5}{6}
n \ge -1\frac{3}{4}
A car rental company charges a flat fee of $24.50 plus $0.40 per mile driven. Maya has a budget of at most $64.50 for her rental. Write and solve an inequality to find the maximum number of miles, m, Maya can drive.
m \le 100
-\frac{4}{9} \div \frac{2}{3}
-\frac{2}{3}
What is a real world scenario that you would rather use an inequality than a equation to model? Why?
Answers may vary
-0.4k \le \frac{3}{5}
k \ge -\frac{3}{2}
-\frac{1}{2}x + 3.8 \le -1.2
x \ge 10
A baker starts with 5 1/2 cups of flour. Each batch of cookies requires 3/4 cup of flour. The baker wants to keep at least 1 3/4 cups of flour remaining. Write and solve an inequality to find the maximum number of batches, b, the baker can make.
b \le 5
-2.5 \times \frac{4}{5} + 3.1
1.1