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# Inequalities 1

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### Inequalities 1

1. 1. Important Facts< means ____ than> means ______ than≤ means ____________________________≥ means ____________________________Use an _____circle for < and > when graphingUse a _______ circle for ≤ and ≥ when graphing
2. 2. Important Facts< means less than> means greater thanUse an open circle for < and > when graphing.Use a closed circle for ≤ and ≥ when graphing
3. 3. How to solve an inequalityThere is only one difference between an equation and an inequality = versus <, >, ≤, ≥
4. 4. Solving inequalities 4 + x < 124 + x < 12 (draw T chart) 4 + x < 12(box in variable) 4 + x < 12 (minus 4 both sides)-4 -4 x<8
5. 5. GraphingWhy a closed circle for ≤ and ≥?If something is on your graph there is a dot or line on it. So, we use a regular dot or line to include numbers in our answer.Why an open circle for < and>? If something is not on our graph we do not put a dot or line on it. So, if 4 is not part of our answer but 3.9999999999… is we can graph that by putting an open circle to show we do not include 4 but we include numbers really really close to 4.
6. 6. Now to graph the solution x<81. Draw a number line. Just need a few numbers on either side of the solution number.2. Decide if open circle or closed circle. Place it above the solution number.3. Determine which way your arrow goes by substituting a number in for the variable to make the statement true. Then draw the arrow pointing in that direction.
7. 7. Solving inequalities 48 ≥ 8 +m48 ≥ 8+m (draw T chart, box variable) -8 -8 (subtract 8 both sides) 40 ≥ m
8. 8. Now to graph the solution 6≥m1. Draw a number line. Just need a few numbers on either side of the solution number.2. Decide if open circle or closed circle. Place it above the solution number.3. Determine which way your arrow goes by substituting a number in for the variable to make the statement true. Then draw the arrow pointing in that direction.
9. 9. 6u ≥ 36 u-6 ≥ 36 +6 + 6 u ≥ 4239 40 41 42 43 44
10. 10. y–1≥5y–1≥5+1 +1 y≥6 3 4 5 6 7 8
11. 11. Graph an inequality x < 12 1) Open circle or closed circle?2) Which direction should the arrow go? 10 11 12 13 14
12. 12. Graph an inequality 42 ≥ m 1) Open circle or closed circle?2) Which direction should the arrow go? 40 41 42 43 44