To solve the inequality \(-12g + 18 > -5g + 53\), we can follow these steps:
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Rearrange the inequality: First, we'll get all the \(g\) terms on one side and the constants on the other side.
\[ -12g + 5g > 53 - 18 \]
This simplifies to:
\[ -7g > 35 \]
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Isolate \(g\): Divide both sides by \(-7\). Remember that dividing or multiplying by a negative number reverses the inequality sign.
\[ g < \frac{35}{-7} \]
Simplifying the fraction gives us:
\[ g < -5 \]
Thus, the solution to the inequality is:
g < -5 (g less than negative 5).