Solving Inequalities What is an inequality An inequality

What is an inequality An inequality is when two things are not equal. In

Technique Always put the variable first. X>10 “x is greater than 10” Or Y<13

Technique Sometimes a variable is not only bigger or smaller than the number but

Possible Solutions Remember a solution is “ a number that can be plugged into

Solving Inequalities are solved the same exact way that equations are. Use the same

The Catch The one tricky item is when you divide by a negative number

Graphing Inequalities get graphed on a number line. X>5 would look like 3 4

Graphing Inequalities If the inequality is < or > then the circle for graphing

Inequalities You are now ready to practice. Be careful with your negative signs and

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Solving Inequalities

What is an inequality An inequality is when two things are not equal. In other words: One thing is bigger than the other thing. 5=7 does not make sense We would use: 5<7 This says “ 5 is less than 7” It compares the two numbers by telling us which one is bigger.

Technique Always put the variable first. X>10 “x is greater than 10” Or Y<13 “y is less than 13 Instead of 4>t you should rewrite it as t<4. NOTE: When you rewrite it you have to reverse the inequality sign.

Technique Sometimes a variable is not only bigger or smaller than the number but it could also be equal to it…. x≥ 5 “x is greater than or equal to 5” This means that x could be any number that is 5 or larger. If it does not have the line under the symbol then it does not include that number in the possible answers.

Possible Solutions Remember a solution is “ a number that can be plugged into the equation to make the whole thing TRUE” X<9 Possible solutions 8, 4, 0, -3. 5. Non-solutions 9, 15, 25 x≤ 14 Possible solutions 14, 12, -5 Non-solutions 15, 26, 37

Solving Inequalities are solved the same exact way that equations are. Use the same thinking and rules. 2 x+5> 27 We are trying to get x by itself. -5 -5 Add/Subtract first 2 x>22 Now divide by 2 2 2 x>11

The Catch The one tricky item is when you divide by a negative number the inequality sign has to flip. -3 x>18 -5 x<40 3 x>-18 -3 -3 -5 -5 3 3 x<-6 x>-8 x>-6 Note how in the first 2 examples the sign flips because we divided by a negative. In the 3 rd example the sign does not flip even though the answer is negative because the action was to divide by a positive 3.

Graphing Inequalities get graphed on a number line. X>5 would look like 3 4 5 6 7

Graphing Inequalities If the inequality is < or > then the circle for graphing is “open” (not filled in) If the inequality is ≤ or ≥ then the circle is closed because it includes that number in the answers. X ≤ 10 versus x < 10 9 10 11

Inequalities You are now ready to practice. Be careful with your negative signs and make sure to write the final inequality with the x first. (x>4 not 4<x)