{"id":10297,"date":"2026-07-03T17:39:42","date_gmt":"2026-07-03T17:39:42","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10297"},"modified":"2026-07-03T17:39:42","modified_gmt":"2026-07-03T17:39:42","slug":"solving-linear-inequalities-including-graphing-techniques","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/solving-linear-inequalities-including-graphing-techniques\/","title":{"rendered":"Solving Linear Inequalities Including Graphing Techniques"},"content":{"rendered":"
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Source: Kapdec.com<\/p>\n<\/div>\n

Unit: Linear inequalities in one or two variables<\/strong><\/h2>\n

Solving Linear Inequalities Including Graphing Techniques<\/strong>
\nOverview<\/strong><\/h3>\n

Linear inequalities are mathematical statements that compare two expressions using inequality symbols such as <, >, \u2264, or \u2265. In one variable, linear inequalities produce a solution set representing a range of values that satisfy the inequality. In two variables, they define regions of the coordinate plane.<\/p>\n

Solving Linear Inequalities in One Variable<\/strong><\/p>\n

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  1. Solving and Graphing:\n
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    • Treat the inequality like an equation when solving.<\/li>\n
    • Graph the solution set on a number line.<\/li>\n
    • Use an open circle for < and > and a closed circle for \u2264 and \u2265.<\/li>\n
    • Draw an arrow indicating the interval where the inequality holds true.<\/li>\n<\/ul>\n<\/li>\n
    • Examples:\n
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      • 2x<\/em>\u22123<5\n
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        • Solve: 2\ud835\udc65<5+3, x<\/em><4<\/li>\n
        • Graph: Open circle at 4, arrow pointing left.<\/li>\n<\/ul>\n<\/li>\n
        • 3\u2212x<\/em>\u22657\n
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          • Solve: 3\u2212\ud835\udc65\u22657, \u2212\ud835\udc65\u22654, \ud835\udc65\u2264\u22124<\/li>\n
          • Graph: Closed circle at -4, arrow pointing right.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

            Solving Linear Inequalities in Two Variables<\/p>\n

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            1. Graphing Technique:\n
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              • Treat the inequality as an equation and graph the corresponding line.<\/li>\n
              • Determine if the region above or below the line (or to the left or right) satisfies the inequality.<\/li>\n
              • Use a dashed line for < or > and a solid line for \u2264 or \u2265.<\/li>\n
              • Test a point in the region to determine shading (e.g., if (0,0) satisfies the inequality, shade that side of the line).<\/li>\n<\/ul>\n<\/li>\n
              • Examples:\n
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                • 2\ud835\udc65+3\ud835\udc66<6\n
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                  • Graph: Plot 2\ud835\udc65+3\ud835\udc66=6 (dashed line), test a point (e.g., (0,0)), and shade below the line.<\/li>\n<\/ul>\n<\/li>\n
                  • 3\ud835\udc65\u22122\ud835\udc66\u22654\n
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                    • Graph: Plot 3x<\/em>\u22122y<\/em>=4 (solid line), test a point (e.g., (0,0)), and shade above the line.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

                      Systems of Linear Inequalities<\/p>\n

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                      1. Graphical Technique:<\/strong>\n
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                        • Graph each inequality separately.<\/li>\n
                        • The solution is the overlapping region of all shaded areas.<\/li>\n<\/ul>\n<\/li>\n
                        • Examples:<\/li>\n<\/ol>\n

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                          Source: Kapdec.com<\/p>\n<\/div>\n

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                          • Graph: Plot x <\/em>+ y<\/em>=4 (shaded below), 2x<\/em>\u2212y<\/em>=1 (shaded above), overlapping shaded area is the solution.<\/li>\n<\/ul>\n

                            Summary<\/p>\n

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                            • Linear inequalities in one variable produce solution sets on number lines, while in two variables, they define shaded regions in the coordinate plane.<\/li>\n
                            • Solving involves treating the inequality as an equation and graphing the solution set or shaded region.<\/li>\n
                            • Systems of linear inequalities can be solved graphically by finding the overlapping shaded regions.<\/li>\n<\/ul>\n

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