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

Question

g>−5 g greater than negative 5 g<−5 g less than negative 5 g<71−17 g less than Start Fraction 71 over negative 17 End Fraction g>71−17

Answer 1

To solve the inequality, we want to isolate the variable g on one side of the inequality.

First, let's subtract -5g from both sides of the inequality to get:
-12g + 18 - (-5g) > -5g + 53 - (-5g)
Simplifying both sides, we have:
-12g + 18 + 5g > 0g + 53

Next, let's combine like terms:
-12g + 5g + 18 > 53

Simplifying the left side of the inequality, we get:
-7g + 18 > 53

Now, let's subtract 18 from both sides of the inequality to isolate the variable g:
-7g + 18 - 18 > 53 - 18
-7g > 35

Next, we divide both sides of the inequality by -7. Since we are dividing by a negative number, the inequality sign will flip:
(-7g)/-7 < 35/-7
g < -5

Therefore, the solution to the inequality is g < -5.