To solve the inequality –3(2x – 5) < 5(2 – x), we can simplify the left and right sides separately and then solve for x:
–3(2x – 5) < 5(2 – x)
–6x + 15 < 10 – 5x
–6x + 5x < 10 – 15
–x < –5
x > 5
The correct representations of the inequality are:
- x > 5
- –6x + 15 < 10 – x
Option A, -6x - 5 < 10 - x, is not correct because it does not correctly simplify the inequality.
Option B, -6x + 15 < 10 - 5x, is correct as it simplifies to -x < -5 after combining like terms.
Option C is not correct because it is the same as option A.
Option D is not correct because it represents the opposite inequality, x < 5 instead of x > 5.
The correct number line representation is the first option: a number line from negative 3 to infinity, with an open circle at 5 and a bold line pointing to the right.