Linear Equation Dcfd56

1. **State the problem:** Solve the equation $$9x + 16 = 6x + 1$$ for $$x$$. 2. **Write the formula and rules:** To solve linear equations, we isolate the variable $$x$$ by performing the same operations on both sides. 3. **Subtract $$6x$$ from both sides:** $$9x + 16 - 6x = 6x + 1 - 6x$$ $$\cancel{9x} + 16 - \cancel{6x} = \cancel{6x} + 1 - \cancel{6x}$$ $$3x + 16 = 1$$ 4. **Subtract 16 from both sides:** $$3x + 16 - 16 = 1 - 16$$ $$3x + \cancel{16} - \cancel{16} = 1 - 16$$ $$3x = -15$$ 5. **Divide both sides by 3:** $$\frac{3x}{3} = \frac{-15}{3}$$ $$\cancel{3}x/\cancel{3} = -5$$ $$x = -5$$ **Final answer:** $$x = -5$$