Question

solve for h.
$-\frac{2}{5}h + 1 = 3 - \frac{1}{2}h + \frac{1}{2}$
$h = $

Explanation:

Step1: Simplify the right side

First, combine the constant terms on the right side. \(3+\frac{1}{2}=\frac{6}{2}+\frac{1}{2}=\frac{7}{2}\). So the equation becomes \(-\frac{2}{5}h + 1=\frac{7}{2}-\frac{1}{2}h\).

Step2: Multiply through by 10 to eliminate fractions

Multiply each term by 10 (the least common multiple of 5 and 2) to get rid of the denominators. \(10\times(-\frac{2}{5}h)+10\times1 = 10\times\frac{7}{2}-10\times\frac{1}{2}h\). Simplifying each term: \(-4h + 10 = 35 - 5h\).

Step3: Add 5h to both sides

Adding \(5h\) to both sides gives \(-4h + 5h+ 10 = 35 - 5h+ 5h\), which simplifies to \(h + 10 = 35\).

Step4: Subtract 10 from both sides

Subtracting 10 from both sides: \(h + 10 - 10 = 35 - 10\), so \(h = 25\).

Answer:

\(25\)