Solving 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

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, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does the solution of a linear inequality represent?

Back

The solution of a linear inequality represents a range of values that satisfy the inequality, often depicted on a number line.

Front

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

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

What is the difference between '<' and '≤'?

Back

'<'' means less than, while '≤' means less than or equal to.

Front

How do you graph a linear inequality on a number line?

Back

To graph a linear inequality on a number line, use an open circle for '<' or '>' and a closed circle for '≤' or '≥', then shade the region that represents the solution.

Front

Solve the inequality: 2x + 3 < 11.

Back

x < 4.

Front

Solve the inequality: -5x ≥ 20.

Back

x ≤ -4.

Front

What does the solution set x < 4 look like on a number line?

Back

An open circle at 4 with a shaded line extending to the left.

Front

Solve the compound inequality: -2 < 3x + 1 < 5.

Back

-1 < x < \\frac{4}{3}.