To solve the equation \( 7h - 5(3h - 8) = -72 \) step by step, we start by simplifying the left side of the equation.
First, we notice there is a term that involves multiplying, specifically \( -5(3h - 8) \). We distribute the negative five across the terms inside the parentheses. This means we multiply negative five by three h and negative five by negative eight. Doing this gives us negative fifteen h and positive forty.
Now, we can rewrite the equation, substituting the expanded form back in. After distributing, our equation looks like this: \( 7h - 15h + 40 = -72 \).
Next, we combine like terms on the left side. We have \( 7h - 15h \), which simplifies to negative eight h. Now our equation reads: \( -8h + 40 = -72 \).
At this point, we want to isolate the term with h. To do this, we will eliminate the positive forty from the left side by subtracting forty from both sides of the equation. By doing this, we adjust the equation to look like this: \( -8h = -72 - 40 \).
Calculating the right side gives us \( -72 - 40 = -112 \). Therefore, the equation now reads: \( -8h = -112 \).
To find h, we need to eliminate the negative eight multiplying it. We can do this by dividing both sides of the equation by negative eight. So now we divide \( -112 \) by \( -8 \).
When we perform that division, we find \( h = 14 \).
We have now solved the equation. The solution is that h equals fourteen.