Answer
$d > \frac{6}{7}$
Work Step by Step
Collect constants on the right side of the inequality by subtracting $5$ from each side:
$-\frac{7d}{3} < -2$
Multiply each side by $3$ to eliminate the fraction:
$-7d < -6$
Divide each side by $-7$ to solve for $d$. Remember that when we divide by a negative number, we need to reverse the sign:
$d > \frac{6}{7}$
We check our answer by first substituting our value for $d$ to check for equality:
$-\frac{7(\frac{6}{7})}{3} + 5$ ? $3$
Simplify the numerator:
$-\frac{6}{3} + 5$ ? $3$
Simplify the fraction:
$-2 + 5$ ? $3$
Add or subtract:
$3 = 3$
Now that we have proven the equality, we need to substitute a value for $d$ such that $d > \frac{6}{7}$. Let's use $1$ for $d$ to plug into the inequality to see if the inequality still holds true:
$-\frac{7(1)}{3} + 5 < 3$
Collect constants on the right side of the inequality:
$-\frac{7(1)}{3} < -2$
Simplify the fraction:
$-\frac{7}{3} < -2$
Convert the fraction to a decimal:
$-2.33 < -2$
