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Hey there! Today we are going to explore inequalities, which are like math's way of comparing things to see who is bigger, smaller, or if they are balanced.
In math, we use equations when things are exactly equal. But in the real world, things are often unequal—like having more than 5 dollars, or needing to be taller than 48 inches to ride a roller coaster!
To show these relationships, we use special symbols. The 'greater than' symbol (>) and 'less than' symbol (<) act like hungry alligator mouths that always open wide to eat the larger number!
We can graph these inequalities on a number line to show all possible answers! An open circle means the starting number is not included (like 'greater than 5'), while a shaded arrow shows all the numbers that work.
Graph the inequality x < 4 on a number line.
- Identify the starting number, which is 4.
- Look at the symbol '<' (less than). Since it doesn't have an 'equal to' line underneath, we will use an open circle at 4.
- Draw an open circle directly on top of the number 4 on your number line.
- Because x is 'less than' 4, we want to shade all the numbers smaller than 4. Draw a bold arrow pointing to the left.
- Double-check your work! Pick a number under your shaded arrow, like 2. Since 2 < 4 is true, your graph is correct!