Which option is the solution to the inequality −12g+18>−5g+53

Question

?(1 point)
Responses

g<−5
g less than negative 5

g>71−17
g greater than Start Fraction 71 over negative 17 End Fraction

g>−5
g greater than negative 5

g<71−17

Answer 1

To solve the inequality \(-12g + 18 > -5g + 53\), we can follow these steps:

1. 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:

   \[ -7g > 35 \]

2. 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).