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

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

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

Back

First, distribute: 3x - 6 < 2x + 18. Then, isolate x: 3x - 2x < 18 + 6, which simplifies to x < 24.

Front

What is the solution to the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then, subtract 10: x > -22.

Front

How do you solve the inequality -13t > 26?

Back

Divide both sides by -13 (remember to flip the inequality): t < -2.

Front

What is the solution to the inequality X - 20 > -30?

Back

Add 20 to both sides: X > -10.

Front

How do you solve the inequality 7(x + 3) < 5x + 13?

Back

Distribute: 7x + 21 < 5x + 13. Then, isolate x: 2x < -8, which simplifies to x < -4.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary value, while non-strict inequalities (≤, ≥) do include the boundary value.

Front

What is the graphical representation of a linear inequality?

Back

A linear inequality is represented on a graph by a shaded region and a boundary line. The line is dashed for strict inequalities and solid for non-strict inequalities.