linear inequality
A linear inequality is an inequality that involves a linear function
A linear inequality is an inequality that involves a linear function. It represents a relationship between two variables that is greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤). The general form of a linear inequality is written as: ax + by < c where a, b, and c are constants, and x and y are variables. In two dimensions, a linear inequality represents a shaded region on a graph. The solution to the inequality is the set of points that satisfy the inequality. If a point lies within the shaded region, it satisfies the inequality. If it lies outside the shaded region, it does not satisfy the inequality. For example, let's consider the inequality 2x + 3y ≤ 12. To graph this inequality, we can turn it into an equation by replacing the inequality symbol (≤) with an equal sign (=): 2x + 3y = 12 Now, we can graph the line 2x + 3y = 12, using any two points that lie on the line. Let's use the points (0, 4) and (6, 0). Plotting these points and connecting them with a straight line gives us the line: __________________ | | * | _____|__________________ Next, we need to determine which side of the line to shade. To do this, we choose a test point that is not on the line. Let's use the point (0, 0) as the test point. Substituting the test point into the inequality, we get: 2(0) + 3(0) ≤ 12 0 ≤ 12 Since this inequality is true, we shade the region that contains the test point. In this case, we shade the region below the line: __________________ | * | | |_____________ | __________________ The shaded region below the line represents all the points that satisfy the inequality 2x + 3y ≤ 12. In summary, a linear inequality is an inequality that involves a linear function. It represents a relationship between two variables and is graphed as a shaded region on a graph. The solution to the inequality is the set of points within the shaded region that satisfy the inequality.
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