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: \(-4 \geq x\).
