Solving and Graphing Linear 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 (>, <, ≥, ≤) instead of an equal sign.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or equal to a specified number.

Front

How do you solve the inequality 10 - 3x < 16?

Back

To solve 10 - 3x < 16, subtract 10 from both sides to get -3x < 6, then divide by -3 (remember to flip the inequality sign) to get x > -2.

Front

What is the solution set for the inequality x ≥ 48?

Back

The solution set for x ≥ 48 includes all real numbers that are 48 or greater.

Front

How do you graph the inequality 3x - 2y < 10?

Back

First, convert to slope-intercept form: y > (3/2)x - 5. Graph the line y = (3/2)x - 5 as a dashed line, then shade above the line.

Front

What does the graph of x < -4 look like?

Back

The graph of x < -4 is a number line with an open circle at -4 and shading to the left, indicating all numbers less than -4.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. It indicates that one value is smaller than another.

Front

How do you interpret the inequality y > 3x - 2?

Back

The inequality y > 3x - 2 means that the value of y is greater than the value of the linear expression 3x - 2.

Front

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

Back

The symbol '>' means 'greater than' and does not include the endpoint, while '≥' means 'greater than or equal to' and includes the endpoint.

Front

How do you solve the inequality 2x + 3 ≤ 11?

Back

To solve 2x + 3 ≤ 11, subtract 3 from both sides to get 2x ≤ 8, then divide by 2 to find x ≤ 4.