Students will learn how to solve equations that require more than two steps. They will solve geometry problems and mathematical ones. Before attempting this section, your students should be very good at simplifying expressions by distributing and combining like terms. They should also have mastered solving two-step equations. Students will also see word problems where the intersection of two lines is found by solving a multi-step equation. Here's an example. Next, give your students this challenge: There is an equilateral triangle, with side lengths \(2x + 1, 3x - 4,\) and \(xy + y - 7.\) What are \(x\) and \(y?\) Here's the solution. After that, give your students this challenge. Finally, give them this one. The only prereq for these challenges is being able to solve multi-step equations.

Next, give your students these challenges:

- Hardest Maths Questions (Junior) - Candles by The How and Why of Mathematics

Solve, assuming \(x\) and \(y\) are natural numbers:

$$6\dfrac{x}{4} \cdot y\dfrac{1}{5} = 20$$Here's the solution:

6 x/4 is between 6 and 7. Thus, y = 3. Next, we substitute, then solve for \(x{:}\)

$$\begin{align} & 6\dfrac{x}{4} \cdot 3\dfrac{1}{5} = 20 \\[1em] & \dfrac{24 + x}{4} \cdot \dfrac{16}{5} = 20 \\[1em] & \dfrac{(24 + x)16}{20} = 20 \\[1em] & (24 + x)16 = 400 \\[1em] & (24 + x)2^4 = 2^4 \cdot 5^2 \\[1em] & 24 + x = 25 \\[1em] & x = 1 \end{align}$$Conclude by leading this investigation:

Fractal Multiplication

by MathPickle