1. **State the problem:** We are given the function $f(x) = 5x + 6$ and asked to find the value of $x$ when $f(x) = 46$. 2. **Write the equation:** Set the function equal to 46: $$5x + 6 = 46$$ 3. **Isolate the variable term:** Subtract 6 from both sides: $$5x + \cancel{6} - \cancel{6} = 46 - 6$$ $$5x = 40$$ 4. **Solve for $x$:** Divide both sides by 5: $$\frac{5x}{\cancel{5}} = \frac{40}{\cancel{5}}$$ $$x = 8$$ 5. **Answer:** The value of $x$ that satisfies $f(x) = 46$ is $x = 8$. This means when you input $8$ into the function $f(x) = 5x + 6$, the output is 46.