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Solve for $b$ . $\newline$ 8(-4b - 9) + 16b < -12 - 20b $\newline$ Write your answer with $b$ first, followed by an inequality symbol. $\newline$ ______

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Solve linear inequalities

Full solution

Q. Solve for

b

.

\newline

8(-4b - 9) + 16b < -12 - 20b

\newline

Write your answer with

b

first, followed by an inequality symbol.

\newline

______

Combine like terms: Now, combine like terms on the left side. $\newline$ $-32b + 16b = -16b$ . $\newline$ So, we get -16b - 72 < -12 - 20b.
Add $b$ terms: Next, add $20b$ to both sides to get all the $b$ terms on one side. $\newline$ $-16b + 20b$ gives $4b$ , and $-20b + 20b$ cancels out. $\newline$ So, we have 4b - 72 < -12.
Isolate $b$ term: Then, add $72$ to both sides to isolate the $b$ term. $\newline$ $4b - 72 + 72$ gives $4b$ , and $-12 + 72$ gives $60$ . $\newline$ So, we have 4b < 60.
Divide to solve: Finally, divide both sides by $4$ to solve for $b$ . $\newline$ $4b / 4$ gives $b$ , and $60 / 4$ gives $15$ . $\newline$ So, we have b < 15.

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