which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? select two options.\nx < 5\n-6x…

Explanation:

Step1: Expand both sides

Expand $-3(2x - 5)$ and $5(2 - x)$ using the distributive property $a(b - c)=ab - ac$. $-3(2x - 5)=-3\times2x-(-3)\times5=-6x + 15$ and $5(2 - x)=5\times2-5\times x = 10-5x$. So the inequality becomes $-6x + 15<10 - 5x$.

Step2: Solve for $x$

Add $6x$ to both sides of the inequality: $-6x+6x + 15<10 - 5x+6x$, which simplifies to $15<10 + x$. Subtract 10 from both sides: $15 - 10<10 - 10+x$, so $x>5$. The number - line representation of $x>5$ has an open - circle at 5 and the arrow points to the right.

Answer:

C. $-6x + 15<10 - 5x$, D. (the number - line with an open - circle at 5 and arrow pointing to the right)