1. **State the problem:** Determine which expressions always yield an even value when $x$ is an even number. 2. **List the expressions:** - Expression A: $\frac{x}{2}$ - Expression B: $9x + 2$ - Expression C: $15 + x$ - Expression D: $\frac{4x}{2}$ 3. **Recall important rules:** - An even number is any integer divisible by 2. - When $x$ is even, $x = 2k$ for some integer $k$. - We will substitute $x=2k$ into each expression and simplify. 4. **Evaluate Expression A: $\frac{x}{2}$** $$\frac{x}{2} = \frac{2k}{2} = \cancel{\frac{2}{2}}k = k$$ Since $k$ can be any integer, $k$ can be even or odd, so $\frac{x}{2}$ is not always even. 5. **Evaluate Expression B: $9x + 2$** Substitute $x=2k$: $$9(2k) + 2 = 18k + 2 = 2(9k + 1)$$ Since $9k + 1$ is an integer, $9x + 2$ is always even. 6. **Evaluate Expression C: $15 + x$** Substitute $x=2k$: $$15 + 2k$$ Since 15 is odd and $2k$ is even, odd + even = odd, so $15 + x$ is always odd, not even. 7. **Evaluate Expression D: $\frac{4x}{2}$** Substitute $x=2k$: $$\frac{4(2k)}{2} = \frac{8k}{2} = \cancel{\frac{8}{2}}k = 4k$$ Since $4k$ is divisible by 2, it is always even. **Final answer:** Expressions that always have an even value when $x$ is even are: - $9x + 2$ - $\frac{4x}{2}$