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.
Answers
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)
Step-by-step 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)
Answer:
C and E
Step-by-step explanation:
Hope this helps! :)