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 A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answer 1

The answer is C and D

Answer 2

The correct statements are:

- 6x + 15 < 10 - 5x ⇒ 3rd answer

An open circle is at 5 and a bold line starts at 5 and is pointing to the right ⇒ 4th answer (attached figure)

Explanation:

∵ The inequality is -3(2x - 5) < 5(2 - x)

At first simplify each side

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember (-)(-) = (+)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Subtract 15 from both sides

∴ - 6x < -5 - 5x

Add 5x to both sides

∴ - x < - 5

Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality

∵ The coefficient of x is -1

∴ Divide both sides by -1

∴ x > 5

The correct statements are:

- 6x + 15 < 10 - 5x ⇒ 3rd answer

An open circle is at 5 and a bold line starts at 5 and is pointing to the right ⇒ 4th answer (attached figure)