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disa
3 months ago
13

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.

Mathematics
2 answers:
lawyer [12.5K]3 months ago
9 0

Response:

C and D

Detailed explanation:

Zina [12.3K]3 months ago
7 0

Answer:

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

Step-by-step explanation:

Given the inequality is -3(2x - 5) < 5(2 - x)

First, simplify both sides:

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember that (-)(-) results in (+)

Thus, -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember that (+)(-) results in (-)

Then, 5(2 - x) = 10 - 5x

Now we have: - 6x + 15 < 10 - 5x

Subtract 15 from both sides

So: - 6x < -5 - 5x

Add 5x to both sides

Thus, - x < - 5

Note that since the coefficient of x is negative, we reverse the inequality sign when dividing both sides by it

∵ The coefficient of x is -1

Therefore, dividing both sides by -1 gives us x > 5

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

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4 0
3 months ago
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Answer:

Clarified below.

Detailed explanation:

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Answer:

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