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5(2h - 6) - 7(h +7) is greater than 4h

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To solve the inequality \( 5(2h - 6) - 7(h + 7) > 4h \), we will first simplify the left side.

  1. Distribute the terms: \[ 5(2h - 6) = 10h - 30 \] \[ -7(h + 7) = -7h - 49 \]

  2. Combine these results: \[ 10h - 30 - 7h - 49 > 4h \]

  3. Simplify the left side further: \[ (10h - 7h) + (-30 - 49) > 4h \] \[ 3h - 79 > 4h \]

  4. Now, isolate \( h \) by moving the \( 4h \) to the left side: \[ 3h - 4h - 79 > 0 \] \[ -h - 79 > 0 \]

  5. Add 79 to both sides: \[ -h > 79 \]

  6. Multiply both sides by -1, and remember to flip the inequality sign: \[ h < -79 \]

Thus, the solution to the inequality is: \[ h < -79 \]