SOLVING FOR A SPECIFIC VARIABLE WORKSHEET

Problem 1 :

Solve the following equation for x.

3x - a  =  kx + b

Problem 2 :

Solve the following equation for h.

A = ½ ⋅ (a + b)h

Problem 3 :

Solve the following equation for h.

C = ⁵⁄₉ ⋅ (F - 32)

Problem 4 :

Solve the following equation for y.

2x + 3y = 18

Problem 5 :

Solve the following equation for x.

2x = ⁽ˣʸ ⁺ ³⁾⁄y

Problem 6 :

Solve the following equation for b.

⁽ᵃ^b ⁻ ¹⁾⁄₃ = c

Problem 7 :

In the formula for perimeter of a rectangle, solve for length.

Problem 8 :

Solve the following equation for k.

n = a + (k - 1)d

Problem 9 :

Solve the following equation for y.

logx + logy = log(x + y)

Problem 10 :

The above equation gives pressure ,P which is exerted by a fluid that is forced to stop moving. The pressure depends on the initial force, ,F and the speed of the fluid, v. Solve for the square of the velocity in terms of the pressure and the force.

Answers

1. Answer :

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₎

2. Answer :

A = ½ ⋅ (a + b)h

Multiply each side by 2.

2A = (a + b)h

Divide each side by (a + b).

²ᴬ⁄₍ₐ ₊ b₎ = h

3. Answer :

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

4. Answer :

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

5. Answer :

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

6. Answer :

⁽ᵃ^b ⁻ ¹⁾⁄₃ = c

Multiply each side by 3. 

ab - 1 = 3c

Add 1 to each side.

ab = 3c + 1

Divide each side by a.

b = ⁽³ᶜ ⁺ ¹⁾⁄ₐ

7. Answer :

Formula for perimeter of a rectangle :

P = 2l + 2w

In the above formula,

P ----> Perimeter

l ----> Length

w ----> Width

Solve the above formula for length (l).

P = 2l + 2w

Subtract 2w from each side.

P - 2w = 2l

Divide each side by 2.

⁽ᴾ ⁻ ²ʷ⁾⁄₂ = l

8. Answer :

n = (k - 1)d

Subtract k from each side. 

n - a = (k - 1)d

Distributive property. 

n - a = kd - d

Add d to each side. 

n - a + d = kd

Divide each side by d. 

⁽ⁿ ⁻ ᵃ ⁺ ᵈ⁾⁄d = k

9. Answer :

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₎

10. Answer :

According to the question, we have to solve for v² in the equation given below.

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