6-43. Determine if each of the numbers below is a solution to the inequality 3x-2lt 2-2x Show all of your work.Homework Help a. 2 b. (1)/(2) c. -3 d. (2)/(3)

To determine if each number is a solution to the inequality $3x-2<2-2x$, we need to substitute the given number into the inequality and check if it satisfies the inequality.<br /><br />a. For $x=2$:<br />$3(2)-2<2-2(2)$<br />$6-2<2-4$<br />$4< -2$ (False)<br /><br />b. For $x=\frac{1}{2}$:<br />$3(\frac{1}{2})-2<2-2(\frac{1}{2})$<br />$\frac{3}{2}-2<2-1$<br />$\frac{1}{2}<1$ (True)<br /><br />c. For $x=-3$:<br />$3(-3)-2<2-2(-3)$<br />$-9-2<2+6$<br />$-11<8$ (True)<br /><br />d. For $x=\frac{2}{3}$:<br />$3(\frac{2}{3})-2<2-2(\frac{2}{3})$<br />$2-2<2-\frac{4}{3}$<br />$0<\frac{2}{3}$ (True)<br /><br />Therefore, the numbers that are solutions to the inequality $3x-2<2-2x$ are $\frac{1}{2}$, $-3$, and $\frac{2}{3}$.