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Solve for j.

–
5≤
–
2j–17
3
<
–
1
Write your answer as a compound inequality with integers.

1 answer

To solve the compound inequality

\[ -5 \leq -2j - 17 < -1, \]

we'll break it into two parts and solve each part separately.

Part 1: Solving \(-5 \leq -2j - 17\)

  1. Add 17 to both sides: \[ -5 + 17 \leq -2j \] \[ 12 \leq -2j \]

  2. Divide both sides by -2 (remember that when dividing by a negative number, the inequality sign flips): \[ \frac{12}{-2} \geq j \] \[ -6 \geq j \quad \text{or} \quad j \leq -6 \]

Part 2: Solving \(-2j - 17 < -1\)

  1. Add 17 to both sides: \[ -2j < -1 + 17 \] \[ -2j < 16 \]

  2. Divide both sides by -2 (again, the inequality sign flips): \[ j > \frac{16}{-2} \] \[ j > -8 \]

Combining the Results

Now we combine the two parts we solved:

\[ -8 < j \leq -6. \]

Thus, the solution in terms of a compound inequality is

\[ -8 < j \leq -6. \]