The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
The given inequality is -3(2x - 5) < 5(2 - x)
We need to simplify the inequality.
<h3>What is inequality?</h3>
In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)
⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]
Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)
⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]
Now, - 6x + 15 < 10 - 5x
By subtracting 15 from both sides, we get
- 6x < -5 - 5x
By adding 5x to both sides, we get - x < - 5
The coefficient of x is -1. So, divide both sides by -1
Then we get x > 5
Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
To learn more about inequalities visit:
brainly.com/question/20383699.
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