1. 1 step inequalities notes Absent copy 4/21

2. Inequality Clues x 3 = x is greater than 3 Graph = x 3 = x is greater than or equal to 3 Graph =

3. Example 1 Solve and graph x + 7 < 10 -7 < -7 0 3 x < 3 -3 0 3 Solution Is this a less than or greater than sign? It is a less than sign. What inverse do we use? We use the inverse of addition and sub. 7 from both sides. What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line face? The line goes to the left because that is the way the arrow points. X < 3

4. Example 2 Solve and Graph -22 > -11 + y +11 > +11 + y -11 0 11 > y y < -11 -21 -17 -11 Solution Is this a less than or greater than sign? ( hint look at the variable) This is a less than or equal too sign. What inverse do we use? We use the inverse of sub. And add 11 to each side. What is the proper way to write the solution? We re-write the solution with the variable first. What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line face? The line goes to the left because the arrow points that direction. y < -11

5. Example 3 Solve and graph 3 > h 5 5 · 3 > h · 5 1 1 5 1 15 > h h < 15 -15 0 15 Solution Is this a less than or greater than sign? ( hint look at the variable ) This is a less than sign. What inverse do we use? We use the inverse of division and mult. by 5 on each side. What is the proper way to write the solution? You write the solution with the variable first What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line face? The line goes to the left. h < 15

6. Example 4 Solve and Graph -3x > -36 -3 -3 x < 12 -12 0 12 Solution Is this a less than or greater than sign? This is a greater than sign. What inverse do we use and what do we have to do to the inequality? ( hint think of the Neg. sign) We use the inverse of mult. and divide by -3 on each side. We have to flip the sign when you mult. Or div. by a neg. # What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line face? The line goes to the left because x is less than or equal too 12. X < 12