Graphing inequalities and solving absolute equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Common symbols include <, >, ≤, and ≥.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the values that satisfy the inequality. It can be shown graphically as a shaded region on a number line or coordinate plane.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line in the solution set.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, set up two separate equations: one for the positive case and one for the negative case. Solve each equation to find the possible solutions.

Front

What is the graphical representation of an absolute value function?

Back

The graph of an absolute value function is a V-shape, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution to a system of inequalities, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean for a region to be shaded in a graph of inequalities?

Back

A shaded region in a graph of inequalities indicates all the points that satisfy the inequality. The shading shows the solution set.

Front

How do you find the boundary line of a linear inequality?

Back

To find the boundary line of a linear inequality, rewrite the inequality as an equation (e.g., y = mx + b) and graph it. The line divides the plane into regions.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where all inequalities overlap.