Questions: Solve for d -2 ≤ (d+6)/3 < 0 Write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

Solution Steps

To solve the compound inequality \(-2 \leq \frac{d+6}{3} < 0\), we need to break it into two separate inequalities and solve each one individually. First, solve \(-2 \leq \frac{d+6}{3}\) by isolating \(d\). Then, solve \(\frac{d+6}{3} < 0\) in a similar manner. Finally, combine the solutions to find the range of values for \(d\) that satisfy both inequalities.

We are given the compound inequality:

\[ -2 \leq \frac{d+6}{3} < 0 \]

This means we need to solve two separate inequalities:

1. \(-2 \leq \frac{d+6}{3}\)
2. \(\frac{d+6}{3} < 0\)

Let's solve the first inequality:

\[ -2 \leq \frac{d+6}{3} \]

Multiply both sides by 3 to eliminate the fraction:

\[ -2 \times 3 \leq d + 6 \]

\[ -6 \leq d + 6 \]

Subtract 6 from both sides:

\[ -6 - 6 \leq d \]

\[ -12 \leq d \]

Now, solve the second inequality:

\[ \frac{d+6}{3} < 0 \]

Multiply both sides by 3:

\[ d + 6 < 0 \]

Subtract 6 from both sides:

\[ d < -6 \]

We have two inequalities:

1. \(-12 \leq d\)
2. \(d < -6\)

Combining these, we get:

\[ -12 \leq d < -6 \]

Final Answer