 # 1.5 Solving Inequalities Remember the rules of solving inequalities.

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1.5 Solving Inequalities Remember the rules of solving inequalities

Properties of Inequality Addition Property of Inequality What you add to one side of the inequality you must add to the other side. This sounds like the Addition property of Equality. Works the same way

Properties of Inequality Multiplication Property of Inequality Here there is a rules you must remember. #1.No zero multiplication #2.If you multiply a positive number the inequality does not move, but if you multiply by a Negative number the sign changes direction The same would work with Division

Lets look a simple problem 5 < 20; multiply by 5 25< 100 still ok Multiply – 2 ; so ( - 2 )25 > (- 2)100 - 50 > - 200 The direction of the inequality switches

Lets use this property to solve 4y – 3 < 5y + 2; Add – 4y and -2 to both sides - 5 < y. The sign did not switch since we did not multiply by a negative number, you may add or subtract any negative number you may want. So the answer is y > -5. I like to have my variable on the left hand side.

When you graph the inequality it is best to have the variable on the left side So y > - 5, can be graphed -5 Solution sets can be written in different notation Set-builder notation { y | y > -5} Interval notation

What is Often called the lazy 8, is the sign for Infinity. Infinity can go in a positive or direction In Interval Notation [ ] are used to show the interval contains the endpoints of the graph and ( ) do not include the endpoints.

Solve Multiply both sides by 2 -2x > x - 7

Solve Multiply both sides by 2 -2x > x – 7 Add – x to both sides -3x > -7

Solve -3x > -7 Multiply both sides by Interval Notation

Homework Page 37 – 38 #15 – 35 odd, # 41 - 43