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Solve for
g.

15+5(7g+17) < 14 g+5+16 g
Write your answer with g first, followed by an inequality symbol.

Solve for $g$ . $\newline$ $15+5(7 g+17)<14 g+5+16 g$ $\newline$ Write your answer with g first, followed by an inequality symbol.

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Solve linear inequalities

Full solution

Q. Solve for

g

.

\newline

15+5(7 g+17)<14 g+5+16 g

\newline

Write your answer with g first, followed by an inequality symbol.

Distribute and Combine Terms: First, we need to simplify both sides of the inequality by distributing and combining like terms. $\newline$ On the left side, distribute the $5$ into the parentheses: $\newline$ $15 + 5(7g + 17) < 14g + 5 + 16g$ $\newline$ $15 + 35g + 85 < 14g + 5 + 16g$ $\newline$ Now combine like terms on the left side: $\newline$ $100 + 35g < 14g + 5 + 16g$
Combine Like Terms: Next, combine like terms on the right side: $\newline$ $100 + 35g < 14g + 5 + 16g$ $\newline$ $100 + 35g < 30g + 5$
Isolate Terms with g: Now, we want to get all the terms with $g$ on one side and the constants on the other side. Subtract $30g$ from both sides: $\newline$ $100 + 35g - 30g < 30g + 5 - 30g$ $\newline$ $100 + 5g < 5$
Subtract Constants: Next, subtract $100$ from both sides to isolate the term with $g$ : $\newline$ $100 + 5g - 100 < 5 - 100$ $\newline$ $5g < -95$
Solve for g: Finally, divide both sides by $5$ to solve for $g$ : $\frac{5g}{5} < \frac{-95}{5}$ $g < -19$

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