which option is the solution to the inequality -12g+18>-5g+53

Answer 1

To solve the inequality \(-12g + 18 > -5g + 53\), we will isolate the variable \(g\).

1. First, let's get all the terms involving \(g\) on one side and the constant terms on the other side. We can do this by adding \(12g\) to both sides:

   \[ 18 > 7g + 53 \]

2. Next, subtract \(53\) from both sides:

   \[ 18 - 53 > 7g \]

   \[ -35 > 7g \]

3. Now, divide both sides by \(7\). When dividing by a positive number, the direction of the inequality remains the same:

   \[ -5 > g \]

or, equivalently,

\[ g < -5 \]

So, the solution to the inequality is:

\[ g < -5 \]