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Find all the values of x such that (4x - 5)/(3x + 5) >= 3

 May 28, 2021
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Find all the values of x such that \(\frac{4x-5}{3x+5} \geq 3\).

 

Keep in mind that an equality can be solved like an equation. The only difference is that whenever we multiply or divide by a negative number, we have to switch the greater than or equal to sign to a less than or equal to sign.

 

We multiply both sides by 3x+5 to get rid of the denominator and get: \(4x-5 \geq 3(3x+5)\).

We then expand out the right hand side: \(4x-5 \geq 9x+15\).

We subtract and add terms to get all the constants (numbers) on one side and all the variables on the other: \(-20 \geq 5x\).
Finally, we divide by 5 to get x by itself: \(-4 \geq x\).

 May 28, 2021

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