02.05 Inequalities
Essential Questions
· How can you create inequalities in one variable and use them to solve problems?
· How can you solve linear inequalities in one variable?
Aninequalitymeans the value of the variable is not equal to one number (like in equations), but instead may be greater than or less than a number.
There are four primary symbols you need to know when working with inequalities.
Indicate what type of circle goes with each inequality symbol
o > Greater than ______
o < Less than ______
o ≥ Greater than or equal to ______
o ≤ Less than or equal to ______
· When you graph an inequality on a number line, there are two questions you must answer.
1. Open or closed circle
2. Shade left or right (When the variable is on the left, like x<5)
Indicate the correct inequality signs that go with the shading indicated:
§ Shade left if ______
§ Shade right if ______
· When multiplying or dividing both sides of an inequality by a negative number, you must flip the inequality symbol.
o -4x > 16 divide each side by -4 and flip the inequality sign and get x<-4
o To prove this must be done just add 4x to each side then subtract 16 from each side and we get ______. Then divide both sides by 4 and get -4 > x. Rearrange the equality so that the variable is on the left and we get ______.
· When solving an inequality follow the order of operations like in an equation
o 3(x+2)<2(x-1) do parentheses first and use the distributive property to get: ______
o Combiner the variable on one side by subtracting 2x on both sides and get: ______
o Subtract 6 from both sides and get: ______
o Graph would be an ______circle on _____with shading to the ______.