what is the solution to -2(8x - 4) < 2x + 5?\no x > \\frac{1}{6}\no x < \\frac{1}{6}\no x > 6\no x < 6

Explanation:

Step1: Expand the left - hand side

Expand $-2(8x - 4)$ using the distributive property $a(b - c)=ab - ac$. Here $a=-2$, $b = 8x$, $c = 4$. So $-2(8x - 4)=-16x+8$. The inequality becomes $-16x + 8<2x+5$.

Step2: Move the $x$ terms to one side

Add $16x$ to both sides of the inequality: $-16x+16x + 8<2x+16x+5$, which simplifies to $8 < 18x+5$.

Step3: Move the constant terms to one side

Subtract 5 from both sides: $8 - 5<18x+5 - 5$, resulting in $3<18x$.

Step4: Solve for $x$

Divide both sides by 18: $\frac{3}{18}<\frac{18x}{18}$, and $\frac{3}{18}=\frac{1}{6}$, so $x>\frac{1}{6}$.

Answer:

A. $x>\frac{1}{6}$