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Solve for h.

19–4h>h+14>
–
4h–6
Write your answer as a compound inequality with integers.

1 answer

To solve the compound inequality \( 19 - 4h > h + 14 > -4h - 6 \), we can break it into two parts and solve each part separately.

Part 1: \( 19 - 4h > h + 14 \)

  1. Start by isolating \( h \): \[ 19 - 4h > h + 14 \]
  2. Bring all terms involving \( h \) to one side and the constant terms to the other side: \[ 19 - 14 > h + 4h \] \[ 5 > 5h \]
  3. Divide by 5: \[ 1 > h \quad \text{or} \quad h < 1 \]

Part 2: \( h + 14 > -4h - 6 \)

  1. Start by isolating \( h \): \[ h + 14 > -4h - 6 \]
  2. Bring all terms involving \( h \) to one side and the constant terms to the other side: \[ h + 4h > -6 - 14 \] \[ 5h > -20 \]
  3. Divide by 5: \[ h > -4 \]

Combine the two inequalities

Now that we have our two inequalities:

  1. \( h < 1 \)
  2. \( h > -4 \)

We can write the solution as a compound inequality: \[ -4 < h < 1 \]

Thus, the answer is: \[ \boxed{(-4, 1)} \]

This indicates that \( h \) is greater than -4 and less than 1.