Linear Inequalities Calculator

What is a Linear Inequality?

A linear inequality is like a math sentence that compares two expressions using symbols like less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥). It's similar to a seesaw - one side might be heavier, lighter, or balanced with the other!

How to Solve Linear Inequalities

Solving linear inequalities is like solving a puzzle. We follow steps to find out what values make the inequality true. It's similar to finding out how much allowance you need to buy your favorite toy!

Formula

A linear inequality looks like this:

\[ ax + b < c \]

Where:

• \(a\) is the coefficient (the number in front of x)
• \(x\) is the variable (what we're solving for)
• \(b\) is the constant on the left side
• \(c\) is the constant on the right side
• \(<\) is the inequality sign (could also be >, ≤, or ≥)

Calculation Steps

1. Move all terms with x to one side of the inequality
2. Move all constant terms to the other side
3. Combine like terms on each side
4. Divide both sides by the coefficient of x
5. If you divided by a negative number, flip the inequality sign

Example and Visual Representation

Let's solve this inequality: 2x + 3 > 7

Step 1: Subtract 3 from both sides: 2x > 4

Step 2: Divide both sides by 2: x > 2

The solution is x > 2

In this picture, the number line shows our solution. The blue arrow points to the right, showing that x can be any number greater than 2. The red text above explains what the picture means.