1. **State the problem:** Determine if each equation is true for one value, all values, or no values of $x$. 2. **Equation 1:** $10 + 3x = -4.2x + 9$ - Combine like terms: $$3x + 4.2x = 9 - 10$$ $$7.2x = -1$$ - Solve for $x$: $$x = \frac{-1}{7.2} = -\frac{5}{36}$$ - Since we found a single value for $x$, this equation is true for **one value**. 3. **Equation 2:** $5(4x + 1) - x = 19x + 5$ - Expand left side: $$20x + 5 - x = 19x + 5$$ - Simplify: $$19x + 5 = 19x + 5$$ - Both sides are identical, so the equation is true for **all values** of $x$. 4. **Equation 3:** $-2(3x - 7) = -6x + 12$ - Expand left side: $$-6x + 14 = -6x + 12$$ - Subtract $-6x$ from both sides: $$14 = 12$$ - This is false, so the equation is true for **no values** of $x$. **Final answers:** - Equation 1: One value - Equation 2: All values - Equation 3: No values