To solve the equation [tex]\( A = \frac{h(b_1 + b_2)}{2} \)[/tex] for [tex]\( b_1 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
A = \frac{h(b_1 + b_2)}{2}
\][/tex]
2. Multiply both sides by 2 to clear the fraction:
[tex]\[
2A = h(b_1 + b_2)
\][/tex]
3. Distribute [tex]\( h \)[/tex] on the right side:
[tex]\[
2A = h b_1 + h b_2
\][/tex]
4. Isolate [tex]\( h b_1 \)[/tex] by subtracting [tex]\( h b_2 \)[/tex] from both sides:
[tex]\[
2A - h b_2 = h b_1
\][/tex]
5. Solve for [tex]\( b_1 \)[/tex] by dividing both sides by [tex]\( h \)[/tex]:
[tex]\[
b_1 = \frac{2A - h b_2}{h}
\][/tex]
6. Simplify the fraction:
[tex]\[
b_1 = \frac{2A}{h} - b_2
\][/tex]
Hence, the solution to the equation for [tex]\( b_1 \)[/tex] is:
[tex]\[
b_1 = \frac{2A}{h} - b_2
\][/tex]
Among the provided options, the correct one is:
[tex]\[
b_1 = \frac{2A}{h} - b_2
\][/tex]
So the correct answer is:
[tex]\[
b_1 = \frac{2A}{h} - b_2
\][/tex]
