Let’s examine what inequalities can tell us.
Is each equation true or false? Be prepared to explain your reasoning.
Noah scored $n$ points in a basketball game.
Draw two number lines to represent the solutions to the two inequalities.
Here is a diagram of an unbalanced hanger.
Jada says that the weight of one circle is greater than the weight of one pentagon.
Write an inequality to represent her statement. Let $p$ be the weight of one pentagon and $c$ be the weight of one circle.
Here is another diagram of an unbalanced hanger.
Graph the solutions to this inequality on a number line.
This is another diagram of an unbalanced hanger.
Andre writes the following inequality: $c + p < s$. Do you agree with his inequality? Explain your reasoning.
Here is a picture of a balanced hanger. It shows that the total weight of the three triangles is the same as the total weight of the four squares.
1. What does this tell you about the weight of one square when compared to one triangle? Explain how you know.
When we find the solutions to an inequality, we should think about its context carefully. A number may be a solution to an inequality outside of a context, but may not make sense when considered in context.
$$12>11$$
$$14\frac12 >11$$
$$130.25 > 11$$
In a basketball game, however, it is only possible to score a whole number of points, so fractional and decimal scores are not possible. It is also highly unlikely that one person would score more than 130 points in a single game.
In other words, the context of an inequality may limit its solutions.
Here is another example:
The solutions to $r<30$ can include numbers such as $27\frac34$, 18.5, 0, and -7. But if $r$ represents the number of minutes of rain yesterday (and it did rain), then our solutions are limited to positive numbers. Zero or negative number of minutes would not make sense in this context.
To show the upper and lower boundaries, we can write two inequalities:
$$0<r$$
$$r<30$$
Inequalities can also represent comparison of two unknown numbers.
