4.1: 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 (e.g., <, >, ≤, ≥).

Front

How do you solve a linear inequality?

Back

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

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

Solve the inequality: 6t + 4 ≤ -2

Back

t ≤ -1

Front

Solve the inequality: x + 5 ≤ 13

Back

x ≤ 8

Front

What is the first step in solving the inequality 2x - 3 > 5?

Back

Add 3 to both sides to isolate the term with the variable: 2x > 8.

Front

What is the solution to the inequality 3x + 1 < 10?

Back

x < 3.

Front

If you multiply or divide both sides of an inequality by a negative number, what happens?

Back

The direction of the inequality sign reverses.

Front

What is the solution set for the inequality x - 4 ≥ 2?

Back

x ≥ 6.