Math Tutoring on Solving Linear Inequalities in Two Variables
When the equal sign in a linear equation is replaced with an inequality sign, a linear inequality is formed.
The solution for a linear equation consists of all points x, y that satisfy the equation. The solution forms a line. However, when we have a linear inequality, the solution consists of all the points that satisfy the inequality but the solution forms a region or half-plane with the line as a border. The line may or may not be included in the solution based upon the inequality symbol. Here are the steps to graphing the solution to a linear inequality.
1. Graph the inequality as if it was a line. However, if the inequality symbol is < or ˃, make a dashed line because the line will not be part of the solution. If the inequality symbol is ≤ or ≥ make a solid line because the line will be part of the solution.
2. Test a point on either side of the line. If the coordinates of the point satisfy the original inequality, shade the same side of the line as the point. If the inequality is false we will shade the other side of the line. There is a shortcut if the inequality is solved for y; you can shade above the line for ˃ or ≥. For < or ≤ shade below the line.
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1. How can a linear equation be converted to linear inequality?
2. What is the difference between solution for a linear equality and linear inequality?
3. How to graph linear inequality?
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