Question

which are correct representations of the inequality $-3(2x - 5) < 5(2 - x)$? select two options.
$square$ $x < 5$
$square$ $-6x - 5 < 10 - x$
$square$ $-6x + 15 < 10 - 5x$
$square$ number line: open circle at 5, arrow pointing right (from 5 through 6, 7)
$square$ number line: open circle at -5, arrow pointing left (from -7 through -6, -5)

Explanation:

Step1: Expand both sides

Expand \(-3(2x - 5)\) to get \(-6x + 15\), and expand \(5(2 - x)\) to get \(10 - 5x\). So the inequality becomes \(-6x + 15 < 10 - 5x\).

Step2: Solve for \(x\)

Add \(6x\) to both sides: \(15 < 10 + x\). Then subtract \(10\) from both sides: \(x > 5\).

Step3: Analyze the number lines

The first number line (with open circle at 5 and arrow to the right) represents \(x > 5\), and the third option \(-6x + 15 < 10 - 5x\) is the expanded form. The option \(x < 5\) is incorrect (we found \(x > 5\)), \(-6x - 5 < 10 - x\) is incorrect expansion, and the last number line represents \(x < -5\) which is incorrect.

Answer:

• \(-6x + 15 < 10 - 5x\)
• The number line with open circle at 5 and arrow pointing to the right (the fourth option in the list)