1. **State the problem:** Solve the equation $46 - 16 - 4 - x = 8 + 13x$ for $x$. 2. **Simplify the left side:** Combine the constants on the left side. $$46 - 16 - 4 = 26$$ So the equation becomes: $$26 - x = 8 + 13x$$ 3. **Isolate variable terms:** Add $x$ to both sides to move all $x$ terms to the right. $$26 - \cancel{x} + x = 8 + 13x + x$$ $$26 = 8 + 14x$$ 4. **Isolate constant terms:** Subtract 8 from both sides. $$26 - 8 = 8 - 8 + 14x$$ $$18 = 14x$$ 5. **Solve for $x$:** Divide both sides by 14. $$\frac{18}{\cancel{14}} = \frac{14x}{\cancel{14}}$$ $$x = \frac{18}{14}$$ 6. **Simplify the fraction:** $$x = \frac{9}{7}$$ **Final answer:** $$x = \frac{9}{7}$$