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

(1 point)
Responses

g < -5
g < -5

g>71−17
g is greater than 71 over negative 17

g > -5

1 answer

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

  1. Move the terms involving \(g\) to one side and the constant terms to the other side: \[ -12g + 5g > 53 - 18 \] This simplifies to: \[ -7g > 35 \]

  2. Now, divide both sides by \(-7\). Remember that when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips: \[ g < \frac{35}{-7} \] Which simplifies to: \[ g < -5 \]

The solution to the inequality is: \[ g < -5 \]

Thus, the correct response is: g < -5.