TWO TRUTHS, ONE LIE Which of the three statements below is a lie? Explain how you made your choice. Explain how you made your choice. The following equations have \( K=-8 \) as a solution: (1) \( 3 x-1=31+x \) (2) \( 4(x+14)=-3 x \) (3) \( \frac{1}{2} x+20=-x(5-3) \)

To determine which statement is a lie, I solved each equation for \( x \) and checked if \( K=-8 \) was a solution. For equation (1) \( 3x - 1 = 31 + x \): - Simplifying gives \( 3x - x = 31 + 1 \) → \( 2x = 32 \) → \( x = 16 \). For equation (2) \( 4(x + 14) = -3x \): - Simplifying gives \( 4x + 56 = -3x \) → \( 4x + 3x = -56 \) → \( 7x = -56 \) → \( x = -8 \). For equation (3) \( \frac{1}{2}x + 20 = -x(5 - 3) \): - Simplifying gives \( \frac{1}{2}x + 20 = -2x \) → \( \frac{1}{2}x + 2x = -20 \) → \( \frac{5}{2}x = -20 \) → \( x = -8 \). Thus, the lie is the first statement because \( K \) only satisfies the second and third equations, but not the first one.