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Solve the inequality -5/2(3x+4)<6-3x

User Jonthan
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1 Answer

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Final answer:

The solution to the inequality -5/2(3x+4)<6-3x is x < 4/7.

Step-by-step explanation:

To solve the given inequality, we'll follow the steps required to isolate the variable x.

First, distribute the -5/2 on the left side of the inequality:

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

Next, add 3x to both sides to get the x terms on one side of the inequality:

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

Combine like terms by finding a common denominator:

(-15x + 6x - 20) / 2 < 6

Now, simplify the left side:

(-9x - 20) / 2 < 6

Multiply both sides by 2 to eliminate the fraction:

-9x - 20 < 12

Add 20 to both sides:

-9x < 32

Finally, divide both sides by -9, remembering to reverse the inequality because we're dividing by a negative number:

x > -32/9

So, the solution to the inequality is x < 4/7.

User Michaelbahr
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