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Solve the inequality-5/2(3x+4)<6-3x. Show your work

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Final answer:

The solution to the inequality is x > -32/9.

Step-by-step explanation:

To solve the inequality -5/2(3x+4) < 6-3x, we need to simplify both sides of the inequality.

Let's start by distributing -5/2 to the expression inside the parentheses on the left side:

-5/2 * 3x - 5/2 * 4 < 6 - 3x

Next, multiply -5/2 by 3x and -5/2 by 4 to get:

-15/2x - 10 < 6 - 3x

To isolate the variable x, let's collect like terms. Add 3x to both sides of the inequality:

-15/2x + 3x - 10 < 6

Simplify the left side of the inequality:

-15/2x + 6/2x - 10 < 6

Combine like terms:

-9/2x - 10 < 6

Add 10 to both sides of the inequality:

-9/2x - 10 + 10 < 6 + 10

Simplify the right side of the inequality:

-9/2x < 16

To get rid of the fraction, multiply both sides of the inequality by -2/9 (the reciprocal of -9/2):

(-2/9)(-9/2x) > (-2/9)(16)

Simplify the left side of the inequality:

x > -32/9

Hence, the solution to the inequality is x > -32/9.

User Tom N
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