1. **Problem:** Solve the equation $4x + 6 = 8x - 10$ using a graph. 2. **Formula and rules:** To solve $4x + 6 = 8x - 10$, we want to find $x$ where the two expressions are equal. This means finding the intersection of the lines $y = 4x + 6$ and $y = 8x - 10$. 3. **Step-by-step solution:** 1. Set the two expressions equal: $$4x + 6 = 8x - 10$$ 2. Subtract $4x$ from both sides: $$6 = 4x - 10$$ 3. Add $10$ to both sides: $$16 = 4x$$ 4. Divide both sides by $4$: $$x = 4$$ 4. **Interpretation:** The solution $x=4$ is where the two lines intersect on the graph. 5. **Verification:** Substitute $x=4$ back into the original equation: Left side: $4(4) + 6 = 16 + 6 = 22$ Right side: $8(4) - 10 = 32 - 10 = 22$ Both sides equal, confirming the solution. **Final answer:** $$x = 4$$