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Solving a Linear Inequality with Distribution. Which represents the solution set to the inequality (-1.5(4x + 1) > 4.5 -2.5(x + 1))?

a) ((-[infinity], -1])
b) ((-[infinity], 7))
c) ((0, [infinity]))
d) (16)

User Bcwhims
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Final answer:

The solution to the linear inequality (-1.5(4x + 1) > 4.5 -2.5(x + 1)) is x < 1/7 or x < 0.142857, and the corresponding solution set is ((-\u221e, -1]).

Step-by-step explanation:

To solve the linear inequality (-1.5(4x + 1) > 4.5 -2.5(x + 1)), we first apply the distributive property:

-1.5 × 4x - 1.5 × 1 > 4.5 - 2.5x - 2.5 × 1

We simplify this to:

-6x - 1.5 > 4.5 - 2.5x - 2.5

Next, we combine like terms and isolate the variable x on one side:

-6x + 2.5x > 4.5 - 1.5 - 2.5

-3.5x > 0.5

Now we divide by -3.5, remembering to flip the inequality sign because we are dividing by a negative number:

x < -0.5 / -3.5

x < 1/7

The solution of the original inequality is x < 1/7, which, in decimal form, is approximately x < 0.142857. Therefore, the correct answer from the options provided is (a) ((-\u221e, -1]) because 0.142857 is less than -1, and we are looking for values less than 0.142857.

User KailuoWang
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