Solve for b. 18 > -6(b + 7) + 12 ______

Distribute and Simplify: First, distribute the -6 across the terms inside the parentheses. Calculation: -6(b + 7) = -6b - 42Add and Simplify: Next, add the distributed terms to the inequality and simplify it. Calculation: 18 > -6b - 42 + 12Combine Like Terms: Combine like terms on the right side of the inequality. Calculation: 18 > -6b - 30Isolate the Term: Now, isolate the term containing b by adding 30 to both sides of the inequality. Calculation: 18 + 30 > -6b - 30 + 30Solve for b: Simplify the inequality after adding 30 to both sides. Calculation: 48 > -6bFinal Solution: To solve for b, divide both sides of the inequality by -6. Remember to reverse the inequality sign because we are dividing by a negative number. Calculation: 48 / -6 < -6b / -6Simplify the inequality to find the value of b. Calculation: -8 < b

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Algebra 1

Solve advanced linear inequalities

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Q. Solve for

b

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18 > -6(b + 7) + 12

Distribute and Simplify: First, distribute the $-6$ across the terms inside the parentheses. $\newline$ Calculation: $-6(b + 7) = -6b - 42$
Add and Simplify: Next, add the distributed terms to the inequality and simplify it. $\newline$ Calculation: 18 > -6b - 42 + 12
Combine Like Terms: Combine like terms on the right side of the inequality. $\newline$ Calculation: 18 > -6b - 30
Isolate the Term: Now, isolate the term containing $b$ by adding $30$ to both sides of the inequality. $\newline$ Calculation: 18 + 30 > -6b - 30 + 30
Solve for $b$ : Simplify the inequality after adding $30$ to both sides. $\newline$ Calculation: 48 > -6b
Final Solution: To solve for $b$ , divide both sides of the inequality by $-6$ . Remember to reverse the inequality sign because we are dividing by a negative number. $\newline$ Calculation: \frac{48}{-6} < \frac{-6b}{-6}
Final Solution: To solve for $b$ , divide both sides of the inequality by $-6$ . Remember to reverse the inequality sign because we are dividing by a negative number. $\newline$ Calculation: \frac{48}{-6} < \frac{-6b}{-6} Simplify the inequality to find the value of $b$ . $\newline$ Calculation: -8 < b