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Solve for m.

–16<m+36≤100
Write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

1 answer

To solve the compound inequality \(-16 < m + 36 \leq 100\), we will break it down into two parts:

  1. \(-16 < m + 36\)
  2. \(m + 36 \leq 100\)

Step 1: Solve the first inequality

\[ -16 < m + 36 \]

Subtract 36 from both sides:

\[ -16 - 36 < m \]

\[ -52 < m \]

This can be rewritten as:

\[ m > -52 \]

Step 2: Solve the second inequality

\[ m + 36 \leq 100 \]

Subtract 36 from both sides:

\[ m \leq 100 - 36 \]

\[ m \leq 64 \]

Step 3: Combine the results

Now we combine the two results:

\[ -52 < m \leq 64 \]

Final Answer:

So the solution as a compound inequality is:

\[ -52 < m \leq 64 \]

This means \(m\) can take any value greater than \(-52\) and up to and including \(64\).