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Linear Inequalities

When is 2x greater than x? Compare algebraic expressions with linear inequalities.

Level 1

         

Which inequality is represented in the above number line?

The above shows how a mobile will be balanced when left to hang. What are the relative weights of these shapes?

Paula Picasso makes her living by painting. She paints small portraits for $20, large landscapes for $50, and masterpieces for $1000.

Paula's goal is to make at least $2800. She has already sold 1 masterpiece and 23 landscapes. How many portraits must she sell to reach her goal?

You should know that

\[ \frac{a}{b} + \frac{c}{d} \ne \frac{a+c}{b+d}.\]

However, if \(a, b, c, d \) are positive integers that satisfy \(\frac{a}{b} < \frac{c}{d},\) what can we say about \(\frac{a+c}{b+d} ?\)

These two numbers are very close together:

\[ \large \frac{122}{353} \approx 0.3456, \ \ \ \ \ \frac{75}{217} \approx 0.3456 \]

Which of these numbers is larger?

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