SOLVING FOR A SPECIFIC VARIABLE

Example 1 :

Solve the following equation for x.

3x - a = kx + b

Solution :

3x - a = kx + b

Subtract kx from each side.

3x - a - kx = b

Add a to each side.

3x - kx = b - a

Distributive property.

x(3 - k) = b - a

Divide each side by (3 - k).

x = ⁽^b ⁻ ᵃ⁾⁄₍₃ ₋ k₎

Example 2 :

Solve the following equation for h.

A = ½ ⋅ (a + b)h

Solution :

A = ½ ⋅ (a + b)h

Multiply each side by 2.

2A = (a + b)h

Divide each side by (a + b).

²ᴬ⁄₍ₐ ₊ b₎ = h

Example 3 : 

Solve the following equation for h. 

C = ⁵⁄₉ ⋅ (F - 32)

Solution :

C = ⁵⁄₉ ⋅ (F - 32)

Multiply each side by ⁹⁄₅. 

⁹^C⁄₅ = F - 32

Add 32 to each side. 

⁹^C⁄₅ + 32 = F

Example 4 : 

Solve the following equation for y.

2x + 3y = 18

Solution :

2x + 3y = 18

Subtract 2x from each side. 

3y = 18 - 2x

Divide each side by 3.

y = ⁽¹⁸ ⁻ ²ˣ⁾⁄₃

y = ¹⁸⁄₃ - ²ˣ⁄₃

y = 6 - ²ˣ⁄₃

Example 5 : 

Solve the following equation for x.

2x = ⁽ˣʸ ⁺ ³⁾⁄y

Solution :

2x = ⁽ˣʸ ⁺ ³⁾⁄y

Multiply each side by y.

2xy = xy + 3

Subtract xy from each side.

xy = 3

Divide each side by y.

x = ³⁄y

Example 6 : 

Solve the following equation for y.

logx + logy = log(x + y)

Solution :

logx + logy = log(x + y)

Use fundamental law of logarithm on the left side of the equation. 

log(xy) = log(x + y)

xy = x + y

Subtract y from each side.

xy - y = x

Use the Distributive property.

y(x - 1) = x

Divide each side by (x - 1).

y = ˣ⁄₍ₓ ₋ ₁₎

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