-12g+18>-5g+53
To solve this inequality, we need to isolate the variable and solve for it.
Starting with the equation:
-12g + 18 > -5g + 53
First, we want to get rid of the variable term on one side of the inequality. We can do this by adding 5g to both sides:
-12g + 5g + 18 > -5g + 5g + 53
Simplifying, we have:
-7g + 18 > 53
Next, we want to isolate the variable term by moving the constant term to the other side of the inequality. We can do this by subtracting 18 from both sides:
-7g + 18 - 18 > 53 - 18
Simplifying, we have:
-7g > 35
Now, to solve for g, we divide both sides of the inequality by -7. However, when dividing by a negative number, we need to change the direction of the inequality sign:
-7g / -7 < 35 / -7
Simplifying, we have:
g < -5
Therefore, the solution to the inequality is g is less than -5.
To solve the inequality -12g + 18 > -5g + 53, we need to isolate the variable g on one side of the inequality sign. Here's how you can do it step by step:
Step 1: Group the terms containing g on one side of the inequality:
Start by subtracting -18 from both sides of the inequality:
-12g + 18 - 18 > -5g + 53 - 18
Simplifying,
-12g > -5g + 35
Step 2: Combine like terms:
Now, let's simplify the right side of the inequality:
-12g > -5g + 35
Combine the -5g and 35:
-12g > -5g + 35
Step 3: Move all terms containing the variable g to one side:
To isolate g on one side, we need to get rid of the -5g term by subtracting -5g from both sides of the inequality:
-12g - (-5g) > -5g - (-5g) + 35
Simplifying,
-12g + 5g > 35
Step 4: Combine like terms:
Combine the -12g and 5g:
-7g > 35
Step 5: Solve for g:
To solve for g, we need to isolate g by dividing both sides of the inequality by -7. However, when dividing an inequality by a negative number, the direction of the inequality sign must be flipped. So, remember to flip the inequality sign:
-7g / -7 < 35 / -7
Simplifying,
g < -5
Therefore, the solution to the inequality -12g + 18 > -5g + 53 is g < -5.