1. Let's start by understanding what an equation is: an equation is a mathematical statement that shows that two expressions are equal, often containing an unknown variable $x$ that we want to find. 2. Real-life situations can be translated into equations by identifying quantities that change or are unknown and relating them with known quantities using mathematical operations. 3. For example, if you want to find out how many apples you have if you buy some more, you can write an equation like $x + 5 = 12$, where $x$ is the number of apples you initially had. 4. To find $x$, you solve the equation by isolating $x$ on one side. For $x + 5 = 12$, subtract 5 from both sides: $$x + 5 - \cancel{5} = 12 - \cancel{5}$$ which simplifies to $$x = 7$$ 5. This means you initially had 7 apples. 6. Another example: If you travel at a speed of 60 km/h for $x$ hours and cover 180 km, the equation is: $$60x = 180$$ Divide both sides by 60: $$\frac{60x}{\cancel{60}} = \frac{180}{\cancel{60}}$$ which simplifies to $$x = 3$$ 7. This means you traveled for 3 hours. 8. To practice, try these equations: - $2x + 3 = 11$ - $5x - 4 = 16$ - $\frac{x}{4} + 7 = 10$ Try to find $x$ by isolating it step-by-step as shown above. Remember, the key is to translate the real-life problem into an equation, then solve for $x$ by performing inverse operations to isolate $x$.