November 12, 2015 Warm-Up:Warm-Up:

Homework Worksheet 1.8T

Objective SWBAT write and solve multi- step inequalities. Write down the objective in your math journal in your own words.

Vocabulary Inequality A mathematical sentence that contains, , or  to show a relationship between quantities. Nathaniel has more than $10 in his wallet. n > $10.00 Jacklynn has run at most 200 miles. j ≤ 200

Good to Know! Inequalities have multiple answers that can make the statement true. In Nathaniel’s example, he might have $20 or $100, all that is known for certain is that he has more than $10 in his wallet. There are an infinite number of possibilities that make the statement n > $10.00 true.

Inequality Symbols

Example 1 Write an inequality for each statement. a.Carla’s weight ( w ) is greater than 100 pounds. w > 100 b.Vicky has at most $500 in her savings account. Let m represent the amount of money in Vicky’s account. m ≤ $500 c.Quinton’s age is greater than 40 years old. Let a represent Quinton’s age. a > 40

Graphing Inequalities Solutions to an inequality can be graphed on a number line. For, use an OPEN circle to graph the inequality: x >  1 x <  1 For  or , use a CLOSED circle to graph the inequality: x   1 x  1x  

Example 2 Solve the inequality and graph its solution on a number line. Graph the solution on a number line. Use a closed circle Inequalities are solved using properties similar to those you used to solve equations.

Solve the inequality and graph its solution on a number line. Graph the solution on a number line. Use an open circle. Example 3 6x + 3 < 2x – 5 –2x –2x a 4x + 3 < –5 a – 3 –3 a 4x < –8 a 4 4 a x < –2 a

Example 4 Solve the inequality.  4x + 7  19  7  7  4x  12  4 x   3  The sign changed direction because both sides were divided by a negative number.