1. **State the problem:** Solve the two-step equation $3x + 4 = 19$ and check the solution. 2. **Formula and rules:** To solve two-step equations of the form $px + q = r$, first isolate the term with $x$ by subtracting or adding $q$ on both sides, then divide both sides by $p$ to solve for $x$. 3. **Step-by-step solution:** - Start with the equation: $$3x + 4 = 19$$ - Subtract 4 from both sides to isolate the term with $x$: $$3x + \cancel{4} - \cancel{4} = 19 - 4$$ $$3x = 15$$ - Divide both sides by 3 to solve for $x$: $$\frac{3x}{\cancel{3}} = \frac{15}{\cancel{3}}$$ $$x = 5$$ 4. **Check the solution:** Substitute $x=5$ back into the original equation: $$3(5) + 4 = 15 + 4 = 19$$ The left side equals the right side, so $x=5$ is correct. **Final answer:** $x = 5$