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$Solve for b. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. 30 b+53 >= 18 b-83$

Solve for $b$ . Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ $30b + 53 \geq 18b - 83$

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Solve multi-step inequalities

Full solution

Q. Solve for

b

. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

\newline

30b + 53 \geq 18b - 83

Isolate variable $b$ : First, we want to isolate the variable $b$ on one side of the inequality. To do this, we will subtract $18$ b from both sides. $\newline$ $30$ b + $53$ - $18$ b \(0\).\(5\)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 - 53 $12b \geq -136$
Divide both sides: Finally, we divide both sides of the inequality by $12$ to solve for $b$ . $\newline$ $\frac{12b}{12} \geq \frac{-136}{12}$ $\newline$ $b \geq \frac{-136}{12}$
Reduce the fraction: We reduce the fraction $-\frac{136}{12}$ to its lowest terms. $\newline$ $b \geq -11\frac{1}{3}$

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