x > 5 is true for 6, for 7, for 5.1, and for infinitely many more.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Showing it on a line
Shade every value that works. An open circle at 5 says 5 itself is not included.
Two variables that move together
At 3 pounds a kilo, cost c and weight w are linked by c = 3w.
Which depends on which
The cost depends on the weight, so weight is independent and cost is dependent.
Many answers instead of one
The inequality n > 5 is true for 6, 7, 5.1, 100 and infinitely many more. Its solution is a range rather than a single number, which is why it is drawn as a stretch of the number line instead of a point.
The four symbols
Greater than, less than, greater than or equal to, and less than or equal to. The two with a line underneath include the endpoint itself. Reading the exact symbol matters, because it decides whether one particular value is a solution.
Where inequalities describe reality better
"You must be at least 12 to ride" is an inequality, not an equation. Speed limits, budgets, capacities and age restrictions are all ranges. Many real constraints are naturally inequalities, and forcing them into equations loses information.
Two variables that move together
When one quantity depends on another, both vary. Writing y = 3x records how: for each value of x there is a matching y. The independent variable is the one you choose; the dependent one follows from it.
Step 2: Try It Yourself
Tap and try it out.
The slope is 3: for every 1 across, the line goes 3 up.
Step 3: Watch an Example
One step at a time.
Watch Leo Describe a Rule
Apples cost 3 pounds a kilo. Leo links weight and cost.
- Step 1
He notices the cost changes when the weight changes, not the other way round.
Step 4: Your Turn
Practice makes it stick.
The Rule
Problem 1 of 2
c = 3w. What is c when w = 7?
The Ride
Problem 2 of 2
You must be over 12 to ride. Is 12 allowed?
Rules and Ranges
1 of 4
c = 5w. What is c when w = 6?
2 of 4
Is 8 a solution of x > 8?
3 of 4
Is 9 a solution of x > 8?
4 of 4
c = 4w. What is c when w = 9?
Step 5: Quick Check
Show what you know.
Question 1 of 2
c = 6w. What is c when w = 8?
Question 2 of 2
How many numbers satisfy x > 5?
What You Learned
- An inequality is true for many values, not one.
- An open circle marks a value that is not included.
- Two linked variables have one that depends on the other.