What is the solution to the inequality −12g+18>−5g+53
To solve the inequality, we need to isolate the variable g on one side of the inequality sign.
Let's start by subtracting -5g from both sides of the inequality:
-12g + 18 - (-5g) > -5g + 53 - (-5g)
This simplifies to:
-12g + 18 + 5g > -5g + 53 + 5g
Combine like terms:
-7g + 18 > 53
Next, let's subtract 18 from both sides:
-7g + 18 - 18 > 53 - 18
This simplifies to:
-7g > 35
Finally, divide both sides by -7 (remember to flip the inequality sign when dividing by a negative number):
(-7g)/(-7) < 35/(-7)
This simplifies to:
g < -5
Therefore, the solution to the inequality -12g + 18 > -5g + 53 is g < -5.