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Solve for j.

–15≤–14j+1+18j≤13
Write your answer as a compound inequality with integers.

1 answer

To solve the compound inequality \(-15 \leq -14j + 1 + 18j \leq 13\), we can start by simplifying the middle expression.

  1. Combine like terms in the middle expression: \[ -14j + 18j = 4j \] So, the compound inequality becomes: \[ -15 \leq 4j + 1 \leq 13 \]

  2. Now we will break this into two inequalities. First, let's solve the left side: \[ -15 \leq 4j + 1 \] Subtract 1 from both sides: \[ -15 - 1 \leq 4j \] \[ -16 \leq 4j \] Now, divide by 4: \[ -4 \leq j \]

  3. Next, solve the right side of the inequality: \[ 4j + 1 \leq 13 \] Subtract 1 from both sides: \[ 4j \leq 13 - 1 \] \[ 4j \leq 12 \] Divide by 4: \[ j \leq 3 \]

  4. Combine the results from both inequalities: \[ -4 \leq j \leq 3 \]

Thus, the solution in compound inequality form is: \[ \boxed{-4 \leq j \leq 3} \]