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 (such as <, >, ≤, or ≥).

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or equal to another value.

Front

What does the symbol '>' represent?

Back

The symbol '>' means 'greater than'. It indicates that one value is larger than another.

Front

How do you represent the solution of a linear inequality on a number line?

Back

The solution is represented by shading the region of the number line that satisfies the inequality, with an open circle for < or > and a closed circle for ≤ or ≥.

Front

What is the solution to the inequality x < -4?

Back

The solution includes all numbers less than -4.

Front

How do you solve the inequality 3(x-2) < 2(x+9)?

Back

Distribute and simplify: 3x - 6 < 2x + 18, then isolate x to find x < 24.

Front

What does a closed circle on a number line indicate?

Back

A closed circle indicates that the number at that point is included in the solution set (used for ≤ or ≥).

Front

What does an open circle on a number line indicate?

Back

An open circle indicates that the number at that point is not included in the solution set (used for < or >).

Front

Solve the inequality: 7(x + 3) < 5x + 13.

Back

x < -4.

Front

Solve the inequality: X - 20 > -30.

Back

X > -10.