Question

solve for h. give an exact answer. 3h = 7(2/7 - 3/7 h) - 10 h =

Explanation:

Step1: Distribute the 7

First, we distribute the 7 on the right side of the equation. Using the distributive property \(a(b - c)=ab - ac\), we have:
\(3h = 7\times\frac{2}{7}-7\times\frac{3}{7}h - 10\)
Simplifying each term: \(7\times\frac{2}{7}=2\) and \(7\times\frac{3}{7}h = 3h\). So the equation becomes:
\(3h=2 - 3h-10\)

Step2: Combine like terms

Next, we combine the constant terms on the right side. \(2 - 10=-8\), so the equation is now:
\(3h=-8 - 3h\)

Step3: Add 3h to both sides

To get all the \(h\) terms on one side, we add \(3h\) to both sides of the equation:
\(3h + 3h=-8-3h + 3h\)
Simplifying both sides: \(6h=-8\)

Step4: Solve for h

Now, we divide both sides by 6 to solve for \(h\):
\(h=\frac{-8}{6}\)
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So:
\(h =-\frac{4}{3}\)

Answer:

\(-\frac{4}{3}\)