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Solve for m.

18–4m>
–
m+3>
–
15–4m
Write your answer as a compound inequality with integers.

1 answer

To solve the compound inequality \( 18 - 4m > -m + 3 > -15 - 4m \), we'll break it down into two parts.

  1. Solve the left inequality: \( 18 - 4m > -m + 3 \)

    Start by isolating \( m \): \[ 18 - 3 > -m + 4m \] \[ 15 > 3m \] Divide both sides by 3: \[ 5 > m \] Or, rewritten: \[ m < 5 \]

  2. Now solve the right inequality: \( -m + 3 > -15 - 4m \)

    Isolate \( m \) again: \[ -m + 4m > -15 - 3 \] \[ 3m > -18 \] Divide both sides by 3: \[ m > -6 \]

Now we have two inequalities:

  1. \( m < 5 \)
  2. \( m > -6 \)

Combining these results provides the compound inequality: \[ -6 < m < 5 \]

Thus, the final answer is: \[ m \in (-6, 5) \]

Or expressed as a compound inequality: \[ -6 < m < 5 \]