Which option is the solution to the inequality −12g+18>−5g+53 ?
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
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.
To solve the inequality −12g + 18 > −5g + 53, you can follow these steps:
Step 1: Combine like terms on both sides of the inequality:
-12g + 18 > -5g + 53
Step 2: Move all the variable terms to one side and the constant terms to the other side by adding 12g and subtracting 53:
-12g + 12g + 18 - 53 > -5g + 12g + 53 - 53
18 - 53 > -5g + 12g
-35 > 7g
Step 3: Divide both sides of the inequality by 7 (since the coefficient of 'g' is 7) to isolate 'g':
-35/7 > 7g/7
-5 > g
So, the solution to the inequality is g < -5.
To find the solution to the inequality −12g + 18 > −5g + 53, we need to isolate the variable g on one side of the inequality sign.
Step 1: Begin by subtracting −18 from both sides to get rid of the constant term on the left side of the inequality:
−12g + 18 - 18 > −5g + 53 - 18
−12g > −5g + 35
Step 2: Next, subtract −5g from both sides to move all terms involving g to the left side:
−12g - (-5g) > −5g + 35 - (-5g)
−12g + 5g > 35
Step 3: Combine like terms on the left side of the inequality:
-12g + 5g = -7g
We now have:
-7g > 35
Step 4: To solve for g, divide both sides of the inequality by -7. Remember that dividing by a negative number reverses the inequality sign:
-7g / -7 < 35 / -7
g < -5
Therefore, the solution to the inequality is g < -5.