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MATHEMATICS FORM 3 LINEAR INEQUALITY BY PN UMRAH BT DALIMUN

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<ul><li>The sign ini linear inequalities </li></ul><ul><li>are: </li></ul><ul><li>greater than </li></ul><ul><li>< less than </li></ul><ul><li>≥ greater than or equal to </li></ul><ul><li>≤ less than or equal to </li></ul>

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Example: <ul><li>5 > 3 </li></ul><ul><li>4 < 7 </li></ul><ul><li>-5 < -3 </li></ul><ul><li>-4 > -7 </li></ul><ul><li>* Known as equivalent inequalities * </li></ul>

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<ul><li>1. A linear inequality on a number line </li></ul><ul><li>a. X > 2 </li></ul><ul><li>1 2 3 4 </li></ul><ul><li>b. X > 6 </li></ul><ul><li>6 7 8 9 </li></ul><ul><li>c. X < -1 </li></ul><ul><li>-4 -3 -2 -1 </li></ul><ul><li>d. X < 10 </li></ul><ul><li>7 8 9 10 11 </li></ul>

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<ul><li>a. X ≥ 3 </li></ul><ul><li>2 3 4 5 6 7 </li></ul><ul><li>b. X ≤ -1 </li></ul><ul><li>-3 -2 -1 0 </li></ul><ul><li>c. X ≥ -8 </li></ul><ul><li>-8 -7 -6 </li></ul><ul><li>d. X ≤ 10 </li></ul><ul><li>7 8 9 10 </li></ul>

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What is the differences between and

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Example of the answers of inequalities: <ul><li>a. X < 5 .: X = 4 , 3 , 2 , 1 , 0 … </li></ul><ul><li>b. X > 3 .: X = 4 , 5 , 6 , 7 , 8 , … </li></ul><ul><li>c. X < 5⅓ .: X = 5 ,4 , 3 , 2 ,1 , … </li></ul><ul><li>d X > 5⅓ .: X = 6 , 7 , 8, 9 , … </li></ul><ul><li>e. X < -4.5 .: X = -5 , -6 , -7 , … </li></ul><ul><li>f. X > -4.5 .: X = -4 , -3 , -2 , -1 , … </li></ul>

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Do the exercise on books

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<ul><li>Choose the correct answer as the example given </li></ul><ul><li>below: </li></ul><ul><li>Example: </li></ul><ul><li>3 + 3 + 3 3³ ( >, < ) </li></ul><ul><li>a. 2/5 1/3 ( > , < ) </li></ul><ul><li>b. 1.2 kg 140 gram ( > , < ) </li></ul><ul><li>c. 6m 40 cm ( > , < ) </li></ul><ul><li>d. 23 31 ( > , < ) </li></ul><ul><li>e. -42 -53 ( > , < ) </li></ul>< click click click click click click click click click click

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CONGRATULATION YOUR ANSWER IS CORRECT

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SORRY! PLEASE TRY AGAIN

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2. Draw the number line to answer the questions: <ul><li>a. X > 2.4 </li></ul><ul><li>b. X < 1.5 </li></ul><ul><li>c. X > 5 </li></ul><ul><li>d. X < 0.2 </li></ul><ul><li>e. X < 5⅓ </li></ul><ul><li>f. X > 2½ </li></ul><ul><li>g. X ≤ 2.4 </li></ul><ul><li>h. X ≥ 2 </li></ul><ul><li>i. X ≥ -1.5 </li></ul>click click click click click click click click click click

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Answer a click 2 3 4 5 6

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Answer b click -2 -1 0 1 2

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Answer c click 5 6 7 8 9

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Answer d click -4 -3 - 2

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Answer e click 1 2 3 4 5 6

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Answer f click 2 3 4 5 6 7

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Answer g click 0 1 2 3

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Answer h click 2 3 4 5 6

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-4 -3 -2 -1 0 1 Answer i click

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<ul><li>New inequalities for a given inequalities when the number is </li></ul><ul><li>added to </li></ul><ul><li>substracted from </li></ul><ul><li>multiply by a number </li></ul><ul><li>divided by a number </li></ul>

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<ul><li>In one operation the inequality must add or substracted or multiply or devide on both side . </li></ul><ul><li>Example: </li></ul><ul><li>1) 2 < 4 [ × 2 ] </li></ul><ul><li>2 × 2 < 4 × 2 </li></ul><ul><li>.: 4 < 8 </li></ul>

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<ul><li>2) 3 > 0 [ ÷ 3] </li></ul><ul><li>3/3 > 0/3 </li></ul><ul><li>.: 1 > 0 </li></ul><ul><li>3) 14 ≥ 7 [ + 2 ] </li></ul><ul><li>14 + 2 ≥ 7 + 2 </li></ul><ul><li>.: 16 ≥ 9 </li></ul><ul><li>4) – 3 ≥ – 4 [ -4 ] </li></ul><ul><li> – 3 – 4 ≥ – 4 – 4 </li></ul><ul><li>.: – 7 ≥ – 8 </li></ul>

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EXERCISES

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<ul><li>1. Represent the following linear inequalities on a number line </li></ul><ul><li>a) p ≤ 5 </li></ul><ul><li>b) d ≥ – 1 </li></ul><ul><li>c)s < – 6 </li></ul><ul><li>d) x ≤ – 10 </li></ul>

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<ul><li>2. Write an inequality based on each number line below </li></ul><ul><li>a. </li></ul><ul><li>-2 -1 0 1 2 </li></ul><ul><li>b. </li></ul><ul><li>6 7 8 9 </li></ul><ul><li>c. </li></ul><ul><li>3 4 5 6 7 </li></ul><ul><li>d. </li></ul><ul><li>-5 -4 -3 -2 -1 0 </li></ul>

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<ul><li>3) Write a linear inequality base on each situation below </li></ul><ul><li>a. It takes shelly move than 20 minutes to </li></ul><ul><li>complete her home work </li></ul><ul><li>b. A force of at least 10 N is required to lift </li></ul><ul><li>the load </li></ul><ul><li>c. To qualify for the 100 M race you must </li></ul><ul><li>clock not more than 11 seconds </li></ul><ul><li>d. The distance from Hisham’s house to the </li></ul><ul><li>bus station is less than 500M </li></ul>

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<ul><li>4) Form a new inequality from the given inequalityby performing the operation stated in brackets . </li></ul><ul><li>a. 4 < 6 [ +5 ] </li></ul><ul><li>b. –3 < 5 [ –2 ] </li></ul><ul><li>c. –10 > –15 [ × – 2 ] </li></ul><ul><li>d. – 4 > – 16 [ ÷ 4 ] </li></ul><ul><li>e. – 2 < 10 [ × – 3 ] </li></ul><ul><li>f. 10 > – 4 [ ÷ – 2 ] </li></ul>

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THE END THANK YOU