Teacher Notes

You do not have to use all examples.If you feel the kids are getting it well, skip

some of the examples and you can do the homework problems in class as guided practice and have them finish it at home.

Activating Prior Knowledge

Plot the following numbers on the number line and label.-7 1.2

AA1CC

Solving Linear Inequalities

in One Variable

Solutions

The solution to an inequality is the set of all numbers that

make the statement true.

Big Ideas (Graphing)

Graphing Practicea. Graph

b.What inequality is the graph representing?

A few more: Write the Inequality the graph is representing

C.

F.E.

D.

Big Ideas (Solving)Use same steps as if you were solving an equation.

While solving your inequality, if you multiply or divide both sides of the inequality by a negative number- reverse (flip) your inequality sign.

#1.Easier (Worked Out) Examples

#2. More Difficult (Worked Out) Example

a. b.

Ex.1 Solve the Inequality and Graph.

𝟓<𝟑 𝐱−𝟐𝟖

Ex.2 Solve the Inequality and Graph.

−𝟒𝟕

𝐫≥−𝟑

Ex.3 Solve the Inequality and Graph.

𝟐 𝒙−𝟔≥𝟑 𝒙−𝟐

Ex.4 Solve the Inequality and Graph.

𝟑 𝒙−(𝟐+𝟔 𝒙)≤𝟐𝟖

Practice #1 Solve and Graph.

a. b. Put them on the same graph in different colors.

Homework

Red Workbookp.90 #1-10 all

Is there always one solution?

No 1. If an ineqality is equivalent to an inequality that is false (Ex. 5>10), then the inequality has no solution.

2. If an inequality is equivalent to an inequality that is true (Ex. -3<0), then the solutions to the inequality are all real numbers.

Ex. 5 Solve the inequality.

a. 14x + 5 < 7(2x-3) b. 12x-1 > 6(2x-1)

Compound Inequalities

A compound inequality consists of two separate

inequalities joined by and or or.

Compound Inequalities Graph Examples

And Or

Worked Out Example: Translating from Words to Inequalities

Ex.1 Translate and Graph

1. All real numbers that are less than -1 or greater than or equal to 4.

2. All real numbers that are greater than or equal to -3 and less than 5

Ex.2 Solve and Graph a Compound Inequality with and

2<x+5<9

You Try!

a. b.

Ex.3 Solve and Graph a Compound Inequality with or

or

You Try!

3h+1<−5𝒐𝒓 2h−5>7

Homework

Red Workbookp.90 #11-23 odd;p.93-94 #4-11 all