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

?(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

1 answer

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).

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