What Are Linear Equations?

Linear equations are equations where the variable (like \( x \)) appears only to the first power and graphs as a straight line. They usually look like \( ax + b = c \).

Solving Linear Equations

To solve, get the variable by itself using inverse operations (like subtracting what’s added, dividing what’s multiplied).

• Step 1: Undo addition or subtraction.
• Step 2: Undo multiplication or division.

What About Inequalities?

Inequalities work like equations, but instead of an \( = \), you use symbols like \( <, >, \leq, \geq \). They tell you if a value is less than, greater than, or equal to something.

When you solve inequalities and multiply or divide by a negative number, remember to flip the sign!

Why Does This Matter?

Linear equations and inequalities are everywhere—from planning budgets to tracking time.

Real-World Connections

• Deciding if you have enough money for a purchase (\( x + 4 \leq 20 \))
• Figuring out how long you can spend on homework if you want to finish before 8 PM.