Q. Solve for b. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.30b+53≥18b−83
Isolate variable : First, we want to isolate the variable on one side of the inequality. To do this, we will subtract from both sides.\newline303030b + 535353 - 181818b \(0\).\(5\)em] \geq \(18\)b - \(83\) - \(18\)b
Simplify both sides: Now, we simplify both sides of the inequality by combining like terms.\(\newline\)\((30b - 18b) + 53 \geq -83\)\(\newline\)\(12b + 53 \geq -83\)
Isolate \(b\) completely: Next, we want to isolate \(b\) completely. To do this, we will subtract \(53\) from both sides of the inequality.\[12b + 53 - 53 \geq -83 - 5312b≥−13612b \geq -13612b≥−136
Divide both sides: Finally, we divide both sides of the inequality by 121212 to solve for bbb.\newline12b12≥−13612\frac{12b}{12} \geq \frac{-136}{12}1212b≥12−136\newlineb≥−13612b \geq \frac{-136}{12}b≥12−136
Reduce the fraction: We reduce the fraction−13612-\frac{136}{12}−12136 to its lowest terms.\newlineb≥−1113b \geq -11\frac{1}{3}b≥−1131