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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 2: Q. 173 (page 144)

Solve the formula $A = \frac{1}{2} h (b_{1} + b_{2})$ for $b_{1}$

Short Answer

Expert verified

The solution for $b_{1}$ is as $b_{1} = \frac{2 A}{h} - b_{2}$ .

Step by step solution

01

Step 1. Given information

The given formula is $A = \frac{1}{2} h (b_{1} + b_{2})$ .

02

Step 2. Simplify the formula.

Multiply both sides of the formula by $2$ and simplify as shown below:

$A = \frac{1}{2} h (b_{1} + b_{2}) 2 脳 A = \frac{1}{2} h (b_{1} + b_{2}) 脳 2 2 A = h (b_{1} + b_{2})$

03

Step 3. Simplify further the formula

Divide both sides by $h$ and simplify as shown below:

$2 A = h (b_{1} + b_{2}) \frac{2 A}{h} = \frac{h (b_{1} + b_{2})}{h} (b_{1} + b_{2}) = \frac{2 A}{h}$

04

Step 4. Simplify further

Subtract $b_{2}$ from both sides and simplify as shown below:

$b_{1} + b_{2} = \frac{2 A}{h} b_{1} + b_{2} - b_{2} = \frac{2 A}{h} - b_{2} b_{1} = \frac{2 A}{h} - b_{2}$

05

Step 5. Final answer

The solution for $b_{1}$ is as $b_{1} = \frac{2 A}{h} - b_{2}$ .

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