Equivalent Expression 4Acfbf

1. **State the problem:** We want to find which expression is equivalent to $24x$ and then solve $24x + 8$. 2. **Check each option for equivalence to $24x$:** - Option 1: $32x$ is not equal to $24x$. - Option 2: $4(6x + 2) = 4 \times 6x + 4 \times 2 = 24x + 8$ which is not equal to $24x$ but equals $24x + 8$. - Option 3: $4(6x + 8) = 24x + 32$ which is not equal to $24x$. - Option 4: $4(6x + 2x) = 4(8x) = 32x$ which is not equal to $24x$. 3. **Conclusion:** None of the options exactly equal $24x$, but option 2 equals $24x + 8$. 4. **Solve $24x + 8$ for $x$ if needed:** If the problem is to solve $24x + 8 = 0$: $$24x + 8 = 0$$ Subtract 8 from both sides: $$24x + \cancel{8} - \cancel{8} = 0 - 8$$ $$24x = -8$$ Divide both sides by 24: $$\frac{24x}{24} = \frac{-8}{24}$$ $$x = -\frac{8}{24}$$ Simplify the fraction: $$x = -\frac{1}{3}$$ **Final answer:** $x = -\frac{1}{3}$ and the expression $4(6x + 2)$ is equivalent to $24x + 8$.