Which option is the solution to the inequality −12g+18>−5g+53−12g+18>−5g+53?(1 point)

Question

Responses

g>71−17g>71−17

g greater than Start Fraction 71 over negative 17 End Fraction

g<71−17g<71−17

g less than Start Fraction 71 over negative 17 End Fraction

g>−5g>−5

g greater than negative 5

g<−5

Answer 1

To solve the inequality \(-12g + 18 > -5g + 53\), we can start by isolating \(g\).

1. Move \(-5g\) to the left side: \[ -12g + 5g + 18 > 53 \] Which simplifies to: \[ -7g + 18 > 53 \]

2. Next, isolate the term with \(g\) by subtracting 18 from both sides: \[ -7g > 53 - 18 \] Which simplifies to: \[ -7g > 35 \]

3. Now divide both sides by -7. Remember that dividing by a negative number reverses the inequality: \[ g < \frac{35}{-7} \] Which simplifies to: \[ g < -5 \]

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

So the correct option is: g < -5.