Linear Inequalities

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a region of the coordinate plane.

'≥' means 'greater than or equal to'. It indicates that the value on the left side of the inequality is either greater than or equal to the value on the right side.

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the coordinate plane.

A solid line indicates that points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

To determine the boundary line, convert the inequality to an equation (replace the inequality sign with an equals sign) and graph that line.

To find the y-intercept, set x = 0 in the equation and solve for y.