To solve for [tex]\( b_1 \)[/tex] in the formula for the area of a trapezoid, we start with the given formula:
[tex]\[
A = \frac{1}{2} \left( b_1 + b_2 \right) h
\][/tex]
Here, [tex]\( A \)[/tex] is the area of the trapezoid, [tex]\( b_1 \)[/tex] and [tex]\( b_2 \)[/tex] are the lengths of the two bases, and [tex]\( h \)[/tex] is the height.
First, we want to isolate the term involving [tex]\( b_1 \)[/tex]. To do this, we will eliminate the fraction by multiplying both sides of the equation by 2:
[tex]\[
2A = \left( b_1 + b_2 \right) h
\][/tex]
Next, we need to solve for [tex]\( b_1 \)[/tex]. To isolate [tex]\( b_1 \)[/tex], divide both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[
\frac{2A}{h} = b_1 + b_2
\][/tex]
Now, subtract [tex]\( b_2 \)[/tex] from both sides to solve for [tex]\( b_1 \)[/tex]:
[tex]\[
b_1 = \frac{2A}{h} - b_2
\][/tex]
Thus, the formula solved for [tex]\( b_1 \)[/tex] is:
[tex]\[
b_1 = \frac{2A}{h} - b_2
\][/tex]
