Answer
$g < 36$
Work Step by Step
Collect constants on the right side of the inequality by subtracting $5$ from each side:
$-\frac{2g}{9} > -8$
Multiply each side by $9$ to eliminate the fraction:
$-2g > -72$
Divide each side by $-2$ to solve for $g$. Remember that when we divide by a negative number, we need to reverse the sign:
$g < 36$
We check our answer by first substituting our value for $g$ to check for equality:
$-\frac{2(36)}{9} + 12$ ? $4$
Simplify the numerator:
$-\frac{72}{9} + 12$ ? $4$
Simplify the fraction:
$-8 + 12$ ? $4$
Add or subtract:
$3 = 3$
Now that we have proven the equality, we need to substitute a value for $g$ such that $g < 36$. Let's use $35$ for $g$ to plug into the inequality to see if the inequality still holds true:
$-\frac{2(35)}{9} + 12 > 4$
Collect constants on the right side of the inequality:
$-\frac{2(35)}{9} > -8$
Simplify the fraction:
$-\frac{70}{9} > -8$
Convert the fraction to a decimal:
$-7.78 > -8$
