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

Using the distributive property \(a(b + c)=ab+ac\), for \(-3(2x - 5)\), we have \(-3\times2x+(-3)\times(-5)=-6x + 15\), and for \(5(2 - x)\), we have \(5\times2-5x=10 - 5x\). So the inequality becomes \(-6x + 15<10 - 5x\).

Step2: Solve the inequality

Add \(6x\) to both sides: \(-6x+15 + 6x<10-5x + 6x\), which simplifies to \(15<10 + x\). Then subtract \(10\) from both sides: \(15-10<10 + x-10\), getting \(x > 5\). The number - line representation for \(x>5\) is a ray starting at \(5\) (open circle) and going to the right.

Answer:

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