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Additional items include X ≤ -110, X > -65, X > -30, and X \u003C 102, using plotted points and shaded/marked intervals on the 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does it mean to express an inequality on a number line?","Question",{"text":62,"@type":63},"The solution marks the set of values that satisfy the inequality by placing/identifying points on the number line and indicating whether endpoints are included or excluded.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How do X > a and X ≥ a differ on a number line?",{"text":67,"@type":63},"X > a uses an open endpoint at a (a not included), while X ≥ a uses a closed endpoint at a (a included).",{"name":69,"@type":60,"acceptedAnswer":70},"What is the difference between X ≤ a and X \u003C a on the number line?",{"text":71,"@type":63},"X ≤ a uses a closed endpoint at a and covers values to the left; X \u003C a uses an open endpoint at a and covers values to the left without including 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        \n1) 46 47 48 49 50 51 52 53 54 55 56 X ≥ 51   \n2) -151 -150 -149 -148 -147 -146 -145 -144 -143 -142 -141 -140 -139 X > -146   \n3) -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90 X > -115   \n4) 45 50 55 60 65 70 75 80 85 90 95 100 105 110 X > 80   \n5) -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 X > -50   \n6) -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 X ≤ -30   \n7) -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 X ≤ -110   \n8) -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 X > -65   \n9) -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 X > -30   \n10) 96 97 98 99 100 101 102 103 104 105 106 107 108 X \u003C 102   \n1-10  90  80  70  60  50  40  30  20  10  0   \n [Math ](Math  www.CommonCoreSheets.com 4)[ www.CommonCoreSheets.com](Math  www.CommonCoreSheets.com 4)[ 4](Math  www.CommonCoreSheets.com 4) ~~                   ~~  \nUse the numberline to express the inequality.  \nEx) -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60  \nX > 0 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n1) 46 47 48 49 50 51 52 53 54 55 56 X ≥ 51   \nX  \n2) -151 -150 -149 -148 -147 -146 -145 -144 -143 -142 -141 -140 -139 X > -146 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~  \n3) -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90 X > -115 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n4) 45 50 55 60 65 70 75 80 85 90 95 100 105 110 X > 80 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n5) -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 X > -50 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n6) -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 X ≤ -30   \nX  \n7) -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 X ≤ -110   \nX  \n8) -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 X > -65 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n9) -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 X > -30 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n10) 96 97 98 99 100 101 102 103 104 105 106 107 108 X \u003C 102 ~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~  \n1-10  90  80  70  60  50  40  30  20  10  0   \n [Math ](Math  www.CommonCoreSheets.com 4)[ www.CommonCoreSheets.com](Math  www.CommonCoreSheets.com 4)[ 4](Math  www.CommonCoreSheets.com 4) ~~                   ~~  \nUse the numberline to express the inequality.  \nEx) X > 0  \n-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60  \n1) X ≥ 51  \n46 47 48 49 50 51 52 53 54 55 56  \n2) X > -146  \n-151 -150 -149 -148 -147 -146 -145 -144 -143 -142 -141 -140 -139  \n3) X > -115  \n-145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90  \n4) X > 80  \n45 50 55 60 65 70 75 80 85 90 95 100 105 110  \n5) X > -50  \n-85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25  \n6) X ≤ -30  \n-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30  \n7) X ≤ -110  \n-170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40","cbCaihl7XQdVO0xL","https://ap.wps.com/l/cbCaihl7XQdVO0xL","pdf",63258,"English","# Use the numberline to express the inequality\n## Strict and inclusive inequalities","[{\"question\":\"What does it mean to express an inequality on a number line?\",\"answer\":\"The solution marks the set of values that satisfy the inequality by placing/identifying points on the number line and indicating whether endpoints are included or excluded.\"},{\"question\":\"How do X \\u003e a and X ≥ a differ on a number line?\",\"answer\":\"X \\u003e a uses an open endpoint at a (a not included), while X ≥ a uses a closed endpoint at a (a included).\"},{\"question\":\"What is the difference between X ≤ a and X \\u003c a on the number line?\",\"answer\":\"X ≤ a uses a closed endpoint at a and covers values to the left; X \\u003c a uses an open endpoint at a and covers values to the left without including a.\"}]","Expressing Inequalities on a Numberline - Use the numberline to express the inequality | PDF"]