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Each problem pairs an inequality with a shown scale or set of tick marks, prompting the learner to identify which points satisfy the condition. Examples include thresholds at values like -27, 140, 54, -190, and others, reinforcing correct placement of open or closed endpoints according to the inequality 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do “\u003C” and “≤” differ when marking answers?","Question",{"text":112,"@type":113},"“\u003C” excludes the boundary value (open endpoint), while “≤” includes it (closed 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140 141 142 143 144 145 146 147 X \u003C 140   \n2) 48 49 50 51 52 53 54 55 56 57 58 59 X ≤ 54   \n3) -197 -196 -195 -194 -193 -192 -191 -190 -189 -188 -187 -186 -185 X ≤ -190   \n4) -180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 X \u003C -120   \n5) 112 113 114 115 116 117 118 119 120 121 122 123 124 X ≥ 117   \n6) -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 X ≤ 50   \n7) -95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 X ≥ -70   \n8) 10 15 20 25 30 35 40 45 50 55 60 X > 35   \n9) -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 X > -170   \n10) -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 X > -150   \n1-10  90  80  70  60  50  40  30  20  10  0   \n [Math ](Math  www.CommonCoreSheets.com 1)[ www.CommonCoreSheets.com](Math  www.CommonCoreSheets.com 1)[ 1](Math  www.CommonCoreSheets.com 1) ~~                   ~~  \nUse the numberline to express the inequality.  \nEx) -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20  \nX ≥ -27   \nX  \n1) 134 135 136 137 138 139 140 141 142 143 144 145 146 147 X \u003C 140 ~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~  \n2) 48 49 50 51 52 53 54 55 56 57 58 59 X ≤ 54   \nX  \n3) -197 -196 -195 -194 -193 -192 -191 -190 -189 -188 -187 -186 -185 X ≤ -190   \nX  \n4) -180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 X \u003C -120 ~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~  \n5) 112 113 114 115 116 117 118 119 120 121 122 123 124 X ≥ 117   \nX  \n6) -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 X ≤ 50   \nX  \n7) -95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 X ≥ -70   \nX  \n8) 10 15 20 25 30 35 40 45 50 55 60 X > 35 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n9) -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 X > -170 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~  \n10) -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 X > -150 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n1-10  90  80  70  60  50  40  30  20  10  0   \n [Math ](Math  www.CommonCoreSheets.com 1)[ www.CommonCoreSheets.com](Math  www.CommonCoreSheets.com 1)[ 1](Math  www.CommonCoreSheets.com 1) ~~                   ~~  \nUse the numberline to express the inequality.  \nEx) X ≥ -27  \n-32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20  \n1) X \u003C 140  \n134 135 136 137 138 139 140 141 142 143 144 145 146 147  \n2) X ≤ 54  \n48 49 50 51 52 53 54 55 56 57 58 59  \n3) X ≤ -190  \n-197 -196 -195 -194 -193 -192 -191 -190 -189 -188 -187 -186 -185  \n4) X \u003C -120  \n-180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70  \n5) X ≥ 117  \n112 113 114 115 116 117 118 119 120 121 122 123 124  \n6) X ≤ 50  \n-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120  \n7) X ≥ -70  \n-95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45","cbCaic0ZSih0SQMf","https://ap.wps.com/l/cbCaic0ZSih0SQMf","pdf",63073,"English","# Express inequalities on a number line\n## Examples and problems","[{\"question\":\"How do “\\u003c” and “≤” differ when marking answers?\",\"answer\":\"“\\u003c” excludes the boundary value (open endpoint), while “≤” includes it (closed endpoint).\"}]","Expressing Inequalities on a Number Line - Use the numberline to express the inequality | PDF"]