1. **State the problem:** Solve the linear equation $$3x + 4 = 9x - 8$$ to find the value of $x$ that makes the statement true. 2. **Write down the formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation by performing the same operations on both sides. 3. **Step-by-step solution:** Start with the equation: $$3x + 4 = 9x - 8$$ Subtract $3x$ from both sides to get all $x$ terms on the right: $$\cancel{3x} + 4 = 9x - \cancel{3x} - 8$$ which simplifies to $$4 = 6x - 8$$ Add $8$ to both sides to isolate the $6x$ term: $$4 + 8 = 6x - 8 + 8$$ which simplifies to $$12 = 6x$$ Divide both sides by $6$ to solve for $x$: $$\frac{12}{\cancel{6}} = \frac{6x}{\cancel{6}}$$ which simplifies to $$2 = x$$ 4. **Final answer:** The value of $x$ that satisfies the equation is $$\boxed{2}$$. 5. **Check the answer:** Substitute $x=2$ back into the original equation: $$3(2) + 4 = 6 + 4 = 10$$ $$9(2) - 8 = 18 - 8 = 10$$ Both sides equal 10, confirming the solution is correct.