Question

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

Answer 1

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:
\[
h < -79
\]