Absolute Value Equations and simple inequalities
Solving Inequalities
Solving Inequalities with Variables on both sides
Solving Compound Inequalities
Solving Absolute Value Inequalities
100
What are the two differences of an equation and an inequality?
1) Equation has an equal sign.Inequality has an greater than, less than signs. 2) When multiplying or dividing my a negative number, you must switch the inequality sign.
100
Solve and graph. (4 + x)/ 3 greater than -4
x greater than -16.
100
Solve and graph. 5 (4 + x) less than or equal to 3 (2 + x)
x is less than or equal to -7.
100
Solve and graph. 11 less than 2x + 3 less than 21.
x is greater than 4 and less than 9.
100
Solve and graph. ab (x - 8) + 5 is greater than or equal to 11.
x is less than or equal to 2 or x is greater than or equal to 14.
200
Define a variable and write an inequality for each situation. Graph the solutions. The maximum speed allowed on Butterfield is 35 mph.
s = speed s less than or equal to 25.
200
Solve and graph. -2 greater than 7x - 2 (x - 4)
x less than -2
200
Solve and graph. 1/2 f + 3/4 is greater than or equal to 1/4 f.
f is greater than or equal to -3.
200
Solve and graph. 2a - 5 less than -5 or 3a - 2 greater than 1.
a less than 0 or a is greater than 1.
200
abs (x + 5) - 4 1/2 is greater than or equal to 7 1/2.
x is less than or equal to -17 or x is greater than or equal to 7.
300
Solve each equation. abs (x - 3) + 14 = 5
no solution
300
Write an inequality for each statement. Solve and graph. One half of a number, increased by 9, is less than 33.
1/2x + 9 less than 33; x less than 48.
300
Solve and graph. 3 (2 - x) is less than -3(x - 1)
no solution.
300
The cruise control function on Sammy's car should keep the speed of the car within 3 miles/hour of the set speed. Write a compound inequality to show the acceptable speeds if the set speed is 55 mi/h.
x is greater than 52 and less than 58.
300
Explain when an abs. value inequality has no solutions or all real solutions.
what was your explanation?
400
Solve. abs (x - 42.04) = 23.24
18.8 and 65.28
400
The product of 4 and the sum of a number and 12 is at most 16.
4 (x + 12) is less than or equal to 16. x is less than or equal to -8.
400
Explain when a simple inequality has no solutions and all real numbers.
What did you say?
400
All real numbers great than 0 and less than 15. Graph this and write the inequality.
x is great than 0 and less than 15.
400
Write an abs. value inequality from the graph on the board.
abs (x - 1) greater than or equal to 3.
500
A thermostat is set so that the temperature in a lab freezer stays within 2.5 degrees F of 2 degrees F. Write and solve an absolute value equation to find the max and min temperatures in the freezer.
abs (x - 2) = 2.5 -0.5 and 4.5 degrees F.
500
Ms. Pak's cable company charges $55 for monthly service plus $4 for each pay per view movie. Mr. Churchill's cable company charges $110 per month with no fees for movies. For what number of movies is the cost of Ms. Pak's company less than the cost of Mr. Churchill's?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or 13.
500
Write an inequality. Solve. Ten less than five times a number is less than six times the number decreased by eight.
5x -10 less than 6x - 8 x greater than -2.
500
One day the high temp. was 95 degrees F and the low temp was 65 degrees F. Write a compound inequality to represent the day's temp.
t is greater than or equal to 64 and less than or equal to 84.
500
On a game show, a player must guess the secret two digit number. The secret number is 23. Write an abs. value inequality that shows that the player's guess is more than 12 numbers away from 23.
abs value (n - 23) is greater than 12.
M
e
n
u