Solving Inequalities using addition or subtraction and Multiplication or division.

3-2 Solving inequalities using addition or subtraction 3-3 Solving inequalities using multiplication or subtraction (You have the hand out for 3-3 that covers solving all inequalities. Please refer to it often. Essential Question 1: How is solving an inequality with addition or subtraction similar to solving an equation? Important vocabulary and key concept: Linear inequality: Equivalent inequality: Addition Property of Inequality Subtraction Property of Inequality When solving an inequality, the goal is always to isolate the variable. This means to get the variable by itself on one side of the inequality symbol. Here is an example: X – 15 > -12 X – > X > 3 So x > 3 is the answer. I can check my work like the examples in the book on page 185.

Essential Question 2: How is solving an inequality with multiplication and division similar to solving an equation? Important vocabulary and key concepts: Multiplication Property of Inequality: Division Property of Inequality: Much like solving an equation, when solving an inequality, you use the multiplication property to undo division and the division property to undo multiplication in order to isolate the variable (get the x by itself on one side). HOWEVER IF YOU MULTIPLY or DIVIDE BOTH SIDES BY A NEGATIVE NUMBER YOU MUST REVERSE THE INEQUALITY SIGN (FLIP THE SIGN). The inequality sign stays the same if you are multiplying or dividing by a positive number, but if that number is a negative, you have to flip the sign. So if the coefficient (number stuck to the variable) is negative, get ready to flip the sign!!! Example: -2x < x > - 7

Answer 1: You can use the addition property to undo subtraction or the subtraction property to undo addition until you isolate the variable. This means that aside from the inequality symbol, we solve inequalities just like equations in our first steps to get the variable by itself on one side. Answer 2: You can use multiplication property to undo division or the division property to undo Multiplication until you isolate the variable. If there is a fraction in the inequality, you can multiply by The reciprocal.