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Example 1: Solve the formula
P = 2L + 2W
for W.
Solution to Example 1
- Given
P = 2L + 2W
- we first isolate the term containing W : add -2L to both sides of the equation
P - 2L = 2L + 2W - 2L
- Simplify to obtain
P - 2L = 2W
- Divide both sides by 2 to obtain W.
W = (P- 2L) / 2
Example 2: Solve the formula
H = sqrt ( x 2 + y 2)
for y, where H, x and y are a positive real numbers and H is greater than x and greater than y.
Solution to Example 2
- Given
H = sqrt ( x 2 + y 2)
- Square both sides
H 2 = x 2 + y 2
- Add - x 2 to both sides and simplify
H 2 - x 2 = x 2 + y 2 - x 2
H 2 - x 2 = y 2
- Solve for y taking the square root
y = + or - sqrt (H 2 - x 2)
- Since y is a positive real number, then y is given by
y = + sqrt (H 2 - x 2)
Example 3: Express F in terms of C in the formula
C = (5 / 9)(F - 32) .
Solution to Example 3
C = (5 / 9)(F - 32)
- Multiply both sides of the formula by 9 / 5
(9 / 5) C = (9 / 5)(5 / 9)(F - 32)
- and simplify
(9 / 5) C = (F - 32)
- Add 32 to both sides of the formula.
(9 / 5) C + 32 = F
- The formula F = (9 / 5) C + 32 expresses F in terms of C.
Example 4: Express y in terms of x in the equation
a x + b y = c , with b not equal to zero..
Solution to Example 4
a x + b y = c
- Add - a x to both sides of the equation
a x + b y - a x = c - a x
b y = - a x + c
- Divide both sides by b.
y = -(a / b) x + c / b
Exercises: Solve each of the fomulas below for the indicated variable.(see answers below).
- A = W L , for L.
- y = m x + b , for x.
- A = (1 / 2)(B + a) , for a.
- S = 2 Pi r h , for r.
- F = (9 / 5)C + 32 , for C.
- 1 / x = 1 / y + 1 / z , for y.
Answers to Above Exercises: Solve each of the fomulas below for the indicated variable.
- L = A / W
- x = (y - b) / m , for m not equal to zero.
- a = 2 A - B
- r = S / (2 Pi h)
- C = (5 / 9)(F - 32)
- y = (x z) / (z - x) , for z not equal to x.
More references and links on how to Solve Equations, Systems of Equations and Inequalities.
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