1. **Problem statement:** We will learn about "Reduktion og ligninger" which means "Reduction and equations" in Danish. This involves simplifying equations and solving for unknown variables. 2. **What is an equation?** An equation is a mathematical statement that two expressions are equal, written as $A = B$. 3. **Goal:** To find the value of the unknown variable (usually $x$) that makes the equation true. 4. **Reduction (Reduktion):** This means simplifying the equation by combining like terms and removing unnecessary parts to make it easier to solve. 5. **Basic rules:** - You can add or subtract the same number on both sides. - You can multiply or divide both sides by the same non-zero number. - Always keep the equation balanced. 6. **Example:** Solve $3x + 5 = 20$ 7. **Step 1:** Subtract 5 from both sides to isolate terms with $x$: $$3x + 5 - \cancel{5} = 20 - \cancel{5}$$ $$3x = 15$$ 8. **Step 2:** Divide both sides by 3 to solve for $x$: $$\frac{3x}{\cancel{3}} = \frac{15}{\cancel{3}}$$ $$x = 5$$ 9. **Answer:** $x = 5$ 10. **Summary:** To solve equations, reduce by simplifying and then isolate the variable using inverse operations while keeping the equation balanced. This is the basic approach to "Reduktion og ligninger" as taught in the Danish curriculum.