Solve Quadratic Inequality: x²-4x+3≤(3x+5)(2x-3)

AI Thread Summary
To solve the quadratic inequality x²-4x+3≤(3x+5)(2x-3), first simplify the right side by using the FOIL method and then rearrange the inequality to have all terms on one side. This will allow you to set the expression to zero, identifying critical values as the roots of the resulting quadratic equation. Once the critical values are found, analyze the intervals created by these roots to determine where the inequality holds true. This approach will help in solving the inequality effectively. Understanding the intervals is crucial for finding the solution set.
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Homework Statement



How to solve this kind of inequality?
x²-4x+3≤(3x+5)(2x-3)

Homework Equations

The Attempt at a Solution

:[/B]
I'm confused. Should I factor the left side or should I FOIL the right side then equate it to zero to find the critical numbers? Help pleaasee.
 
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Simplify the inequality and arrange for all terms to be on one side and 0 on the other side. The quadratic inequality can then be examined for the three intervals on x. The critical values will be the roots of the simplified quadratic expression.
 

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