Solving Inequalities Equations

If you read from left to right 10 “is greater than “ 5 X

If you read from right to left 5 “is less than “ 10 X

If you read from left to right 5 “is less than “ 10 X

If you read from right to left 10 “is greater than“ 10 X

. Number line X is equal to 7 Therefore you include the 7 with a dotted cirle.

Number line .

. Number line X is equal to -3 Therefore you include the -3 with a dotted circle.

Number line .

. Number line X is greater equal to -2 Therefore you include the -2 with a dotted circle. You draw and arrow to the right

Number line .

O Number line X is greater than 2 Therefore you do not include the 2 with an open circle. You draw and arrow to the right

Number line O

. Number line X is less than equal to -6 Therefore you include the -6 with an dotted closed circle You draw and arrow to the left

Number line .

O Number line X is less than -6 Therefore you do not include the -6 with an open circle You draw and arrow to the left

Number line O

> Greater Than Equal To Inequality Symbols Open Circle indicates Not Equal > Greater Than > Greater Than Equal To Closed Circle indicates Equal To < Less Than Open Circle indicates Not Equal < Less Than Equal to Closed Circle indicates Equal To

Solving Inequality Equations X + 5 = 13 What Side of the equation you are going to work with ? The Rights side The lefts side

Solving Inequality Equations X + 5 > 13 What Side of the equation you are going to work with ? The Rights side The lefts side

Solving Inequality Equations X + 5 > 13 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

Solving Inequality Equations X + 5 > 13 -5 -5 _________ You subtract – 5 in both side of the equatiion .

Solving Inequality Equations X + 5 > 13 _________ - 5 - 5 X > 8 You drop down the X. Cancel 5 Drop down “>“ sign. And then subtract 13 – 5 = 8.

Solving Inequality Equations X + 5 > 13 . _________ - 5 - 5 X > 8 X is Greater than equal to 8 Therefore you include the 8 with a closed circle You draw and arrow to the right

Solving Inequality Equations 2x < 18 What Side of the equation you are going to work with ? The Rights side The lefts side

Solving Inequality Equations 2x < 18 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

Solving Inequality Equations ___ 2x < 18 __ _________ 2 2 1 x 9 < You divide by 2 in both side. Now 2 divide 2 gives you 1 x. You drop down “ <“ Now add 18 2 gives you 9. ÷

Solving Inequality Equations ___ 2x < 18 __ _________ 2 2 1 x 9 < O X is Less than 9 Therefore you do not include the 9 with an opened circle You draw and arrow to the left

Solving Inequality Equations x 4 > - 2 What Side of the equation you are going to work with ? The Rights side The lefts side

Solving Inequality Equations x 4 > - 2 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

Solving Inequality Equations x 4 4• > - 2 •4 ___________ 1 x > -8 You multiply by 4 in both side. Now 4 divide 4 gives you 1X. You drop down “>“ Now -2 multiply by 4 equals -8.

Solving Inequality Equations x 4 4• > - 2 •4 . ___________ 1 x > -8 X is Greater equal to -8 Therefore you do include the -8 with an closed circle You draw and arrow to the right

In Inequalities there are two cases you Need to Flip The Sign

When you multiply or divide by a negative number Flip the Sigh of Inequality

Solving Inequality Equations - 5X - 3 > 12 What Side of the equation you are going to work with ? The Rights side The lefts side

Solving Inequality Equations - 5X - 3 > 12 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

Solving Inequality Equations - 5X - 3 > 12 ___________ +3 +3 -5X > 15 You add by 3 in both side. You drop down -5x Cancel 3 You drop down > Now 12 plus 3 gives you 15.

Solving Inequality Equations - 5X - 3 > 12 ___________ +3 +3 -5X > __ 15 __ -5 -5 ___________ 1 x < - 3 Now divide by -5 in both sides Now -5 divide -5 gives you 1X. You drop down “ >“ and flip the sign Now 15 divide by 5 equals -3

Solving Inequality Equations - 5X - 3 > 12 ___________ +3 +3 -5X > __ 15 __ -5 -5 ___________ 1 x < - 3 O

Second Case when you flip the Inequalities Sign When the variable is in the right side of the equation Change it to the left side. X

Second Case when you flip the Inequalities Sign When the variable is in the right side of the equation Change it to the left side. X And Flip the sign

Solving Inequality Equations - 44 < - 8 + 6X +8 +8 ___________ 6X 36 < You add + 8 in both side. Now -44 plus 8 gives you -36. You drop down “ < “ Cancel 8 Now You drop down 6x

Solving Inequality Equations - 44 < - 8 + 6X ___________ +8 +8 6X 36 __ < __ ___________ 6 6 6 < 1 X Now divide by 6 in both sides Now 36 divide 6 gives you 6. Drop < and 6 divide 6 gives you 1X.

Solving Inequality Equations - 44 < - 8 + 6X ___________ +8 +8 6X 36 __ < __ ___________ 6 6 6 < 1 X

Solving Inequality Equations - 44 < - 8 + 6X ___________ +8 +8 6X 36 __ < __ ___________ 6 6 6 < X

Solving Inequality Equations - 44 < - 8 + 6X ___________ +8 +8 6X 36 __ < __ ___________ 6 6 > 6 X

Solving Inequality Equations - 44 < - 8 + 6X ___________ +8 +8 6X 36 __ < __ . ___________ 6 6 > 6 X

Compound Inequalities A compound inequality consists of two inequalities that are joined together by the word "and" or the word "or". x > -3 and x < 5

Compound Inequalities A compound inequality consists of two inequalities that are joined together by the word "and" or the word "or". x > -3 and x < 5

Compound Inequalities x > -3 and x < 5

Compound Inequalities x > -3 and x < 5 X>-3 O X<5 O

Compound Inequalities x > -3 and x < 5 X>-3 O X<5 O O O

Compound Inequalities x > -3 and x < 5 X>-3 O X<5 O O O

Compound Inequalities x > -3 and x < 5 O O

Compound Inequalities x < -3 or x > 5 X<-3 X > 5 O O NO SOLUTION

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 Solve the Two Inequalities Independently

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 Solve the Two Inequalities Independently 10< 2x + 8 and 2x + 8< 16

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 10< 2x + 8 and 2x + 8< 16

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 10< 2x + 8 2x + 8< 16 and ______ ______ -8 - 8 -8 -8 2 < 2x 2x < 8 __ __ __ __ ______ ______ 2 2 2 2 4 1 < x < x x > 1

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 10< 2x + 8 2x + 8< 16 and ______ ______ -8 - 8 -8 -8 2 < 2x 2x < 8 __ __ __ __ ______ ______ 2 2 2 2 4 1 < x < x x > 1

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 x < 4 x > 1

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 O

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 O . O

Compound Inequalities - Example 1 Solve and Graph the following Inequality 10< 2x + 8< 16 O . O