1. **Problem:** Solve the equation $7x + 15 = 5$ using the bar model method. 2. **Formula and rules:** To solve linear equations like $ax + b = c$, we isolate $x$ by performing inverse operations: subtract $b$ from both sides, then divide both sides by $a$. 3. **Step-by-step solution:** 1. Start with the equation: $$7x + 15 = 5$$ 2. Subtract 15 from both sides to isolate the term with $x$: $$7x + \cancel{15} - \cancel{15} = 5 - 15$$ $$7x = -10$$ 3. Divide both sides by 7 to solve for $x$: $$\frac{7x}{\cancel{7}} = \frac{-10}{\cancel{7}}$$ $$x = -\frac{10}{7}$$ 4. **Explanation:** - We first removed the constant term 15 by subtracting it from both sides. - Then, to isolate $x$, we divided both sides by the coefficient 7. - The bar model visually represents the parts of the equation, showing the whole and parts to help understand the inverse operations. 5. **Final answer:** $$x = -\frac{10}{7}$$