Chapter 8: Inequalities 8.1 Equations and Inequalities 8.2 Solving One- step Inequalities 8.3 Solving two step inequalities

8.1 Equations and Inequalities In this lesson you will learn: -to graph an inequality -to recognize the difference between the graph of an equality and the graph of an inequality Words to learn inequality symbols: ( <, <, >, >) these show the relationship ___________ equality expressions Need to know: < means “__________ ________” < means “ ______ ______ ____ _________ _____” > Means “ __________ ________” > means “ __________ _____ ___ _______ _____”

Graphing on a number line ** The solution to an equation can be graphed on a number line. A solid black dot at 2 represents the solution to the equation x = 2 ** The solution to an inequality can also be graphed on a number line. Look at the graphs below. An arrow continues in either direction (left or right) indefinitely! (forever) All the numbers in that direction are included in the solution. These numbers make up the solution set. The number at the endpoint of each arrow is included (closed dot) in an inequality with < or >. The number at the endpoint is NOT INCLUDED (open dot) in an inequality with < or >.

Example: Solve the inequality x + 3 < 5 ***Think of all the possible values of x. The values { -3, -2, -1, 0, 1} make the inequality true. The values { 2, 3, 4, 5, 6} make the inequality false. Focus on the idea To graph an inequality, draw an arrow to indicate the direction of the solution. Draw an open or closed dot to indicate whether or not the endpoint is included.

Write the inequality that is graphed on the number line. ** First look at the open ( < or > ) or closed dot ( < or > ) then the numbers

18 > 4 + q 2) - 14 > x – 1

3) – 11 > y + 1 4) 11 < d + 2

5 < w + 9 - 5 + p > 5 g – 9 > 14

f + 6 < 9 -6 < - 3 + a 8 > n – 4

5x + 2 < 17 21 < 3 + 9x

9 – x > 10 SKIP THIS ONE 27 < 7x + 6