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# Linear Inequalities This document discusses solving and graphing linear inequalities. It provides examples and explains the steps involved. **Key Concepts:** * **Inequalities:** Similar to equations, but use symbols like , ≤, ≥. * **Ordered Pairs:** Used to represent solutions that satisfy the...

# Linear Inequalities This document discusses solving and graphing linear inequalities. It provides examples and explains the steps involved. **Key Concepts:** * **Inequalities:** Similar to equations, but use symbols like , ≤, ≥. * **Ordered Pairs:** Used to represent solutions that satisfy the inequality. * **Slope-Intercept Form:** The form $y = mx + b$ is used to graph the inequality. * **Dashed vs. Solid Lines:** Dashed lines are used for inequalities with < or >, solid lines for ≤ or ≥. **Examples:** The example provided focuses on solving and graphing the inequality 2x - 3y < 15. * **Steps to Solve:** The example shows plugging in values to verify solutions. * **Graphing:** The notes indicate that for inequalities, one uses slope-intercept form to graph, such as putting the inequality into the form $y = mx+c$. **Summary of procedure:** 1. **Convert to Slope-Intercept Form:** Put the inequality into the form $y = mx + b$. 2. **Determine Line Type:** If the inequality is < or >, draw a dashed line. If ≤ or ≥, draw a solid line. 3. **Test a Point to Determine the Region:** Pick a point not on the line and substitute the coordinates into the original inequality, to determine whether the point should be included in the solution set. 4. **Shade the Appropriate Region:** Shade the region containing the point that satisfies the inequality. The document provides general instructions for manipulating inequalities and provides examples of applying these rules to linear inequalities.