Linear and Systems of Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

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

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables that are solved together.

Front

How do you find the solution to a system of inequalities?

Back

To find the solution to a system of inequalities, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What is the difference between '>' and '≥'?

Back

The symbol '>' means 'greater than' (not including the value), while '≥' means 'greater than or equal to' (including the value).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert a linear equation to slope-intercept form?

Back

To convert a linear equation to slope-intercept form, solve for y in terms of x.