December 14, 2012 GLE 16- Inequalities Do Now: What is an INEQUALITY?

Inequalities Algebraic Problem Compares Unequal expressions So, What is an expression? no equal sign each side of the inequality Simplify Isolate variable (get the variable alone)

Inequalities Use symbols Do you know symbols we should use? < >

What Do the Symbols Mean? < less than > greater than < less than or equal to > greater than or equal to

Inequalities Remember: FLIP the inequality sign if you multiply or divide both sides by a negative number < would be changed to > > would be changed to < > would be changed to < < would be changed to >

What is my next step? When Do I Flip My Sign? -5x + 42 < 17 Write the Problem What is my next step?

Step 2 Use inverse operations (opposite operation) to solve for x (the unknown- the variable) -5x + 42 – 42 < 17 – 42 (subtract 42 from both sides)

Step 3 -5x < -25 -5x < -25 -5 -5 (divide both sides by -5)

Step 4 What is my answer? The solution to the inequality is X > 5 (Remember to flip the sign) X is greater than five This means that x represents all numbers greater than 5

How Do I Solve an Inequality? Write the Problem P – 4 > 7 What is my next step?

Next step P – 4 + 4 > 7 + 4 (add 4 to both sides) Am I finished?

What is my solution? P > 11 The solution to the inequality is p > 11

What are characteristics of an inequality? Variable Mathematical operation (addition, subtraction, multiplication, division) Inequality sign

Solving Inequalities Write the Problem 2x – 4 < 10 What is my first step?

Solve for x First, add 4 to both sides 2x – 4 + 4 < 10 + 4

What is my next step? 2x < 14 Divide both sides by 2

What is my answer? The solution to the inequality is: X < 7 The variable represents all numbers less than 7

Practice with Negatives Write the Problem -2x – 4 < 10

What is the next step? Examine the problem…… Explain (in words) the steps that need to be taken to isolate (separate) the variable Identify any/all operations and signs

Inverse Operations -2x – 4 + 4 < 10 + 4 Add 4 to both sides of the problem (inequality) -2x < 14

-2x < 14 Divide both sides by -2 -2x /-2 < 14 / 2

Remember………………. The inequality is being divided by a negative number The inequality symbol switches directions So, how would I write my solution?

Solution X < -7

Graph Inequalities How do I get started?

Graphing A number line is used to graph inequalities with one variable

Read < as “less than” How do I read the graph? Read < as “less than”

Read > as “greater than” Reading a Graph Read > as “greater than”

Read < as “less than or equal to” Reading a Graph Read < as “less than or equal to”

Read > as “greater than or equal to”. Read a Graph Read > as “greater than or equal to”.

Methods to Graphing Open Dot One is NOT part of a solution

Closed Dot Shows that the number is part of the solution Methods to Graphing Closed Dot Shows that the number is part of the solution

Individual Practice (WORK INDIVIDUALLY- BY YOURSELF) 6 > 2x R + 9 > 24 12 – 12n > -48 18 < 18y – 18

Solve Graph Each Inequality

Closing Up What is an inequality? What are the parts of an inequality? What symbols do we use for inequalities?