Question

solve for b.
reduce any fractions to lowest terms. dont round your answer, and dont use mixed fractions.
30b + 53 ≥ 18b - 83

Explanation:

Step1: Subtract \(18b\) from both sides

To isolate the terms with \(b\) on one side, we subtract \(18b\) from both sides of the inequality \(30b + 53 \geq 18b - 83\). This gives us \(30b - 18b + 53 \geq 18b - 18b - 83\), which simplifies to \(12b + 53 \geq -83\).

Step2: Subtract 53 from both sides

Next, we subtract 53 from both sides to get the term with \(b\) alone on the left. So, \(12b + 53 - 53 \geq -83 - 53\), which simplifies to \(12b \geq -136\).

Step3: Divide both sides by 12

Now, we divide both sides of the inequality \(12b \geq -136\) by 12 to solve for \(b\). This gives \(b \geq \frac{-136}{12}\). We can simplify the fraction \(\frac{-136}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So, \(\frac{-136\div4}{12\div4}=\frac{-34}{3}\).

Answer:

\(b \geq -\frac{34}{3}\)