Question

which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? select two options. x < 5 -6x - 5 < 10 - x -6x + 15 < 10 - 5x

Explanation:

Step1: Expand both sides

Expand $-3(2x - 5)$ and $5(2 - x)$.
$-3(2x - 5)=-6x + 15$ and $5(2 - x)=10 - 5x$. So the inequality becomes $-6x + 15<10 - 5x$.

Step2: Solve for $x$

Add $6x$ to both sides: $15<10 + x$.
Subtract 10 from both sides: $x > 5$.
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)