SOLVING LITERAL EQUATIONS WORKSHEET

Problem 1 :

Solve for w in the formula for area of a rectangle : 

A  =  l ⋅ w

Problem 2 :

Solve for c in the formula for Einstein’s Theory of Relativity : 

E  =  mc²

Problem 3 :

Solve for h in the formula for the surface area of a right cylinder :

S  =  2∏r(h + r)

Problem 4 : 

Solve for r in the formula for volume of sphere :

V  =  4/3 ⋅ ∏r³

Problem 5 :

Solve for w in the formula for perimeter of the rectangle :

P  =  2(l + w)

Problem 6 :

Solve for a :

Q  =  3a + 5ac

Problem 7 : 

Solve for b₁ :

A  =  1/2 ⋅ h(b₁ + b₂)

Problem 8 : 

Solve for b :

a² + b²  =  c²

Detailed Answer Key

Problem 1 :

Solve for w in the formula for area of a rectangle : 

A  =  l ⋅ w

Solution : 

A  =  l ⋅ w

Divide each side by l.

A / l  =  w

Problem 2 :

Solve for c in the formula for Einstein’s Theory of Relativity : 

E  =  mc²

Solution : 

E  =  mc²

Divide each side by m.

E / m  =  c²

Take square root on each side. 

√(E/m)  =  √c²

√(E/m)  =  c

Problem 3 : 

Solve for h in the formula for the surface area of a right cylinder :

S  =  2πr(h + r)

Solution : 

S  =  2πr(h + r)

Use distributive property of multiplication over addition. 

S  =  2πrh + 2πr²

Subtract 2∏r² from each side. 

S - 2πr²  =  2πrh

Divide each side by 2∏r. 

(S - 2πr²) / 2πr  =  h

Problem 4 : 

Solve for r in the formula for volume of sphere :

V  =  4/3 ⋅ πr³

Solution : 

V  =  4/3 ⋅ πr³

Multiply each side by 3/4. 

3V/4  =  πr³

Divide each side by ∏.

3V/4π  =  r³

Take cube root on each side. 

³√(3V/4π)  =  ³√r³

³√(3V/4π)  =  r

Problem 5 :

Solve for w in the formula for perimeter of the rectangle :

P  =  2(l + w)

Solution : 

P  =  2(l + w)

Use distributive property of multiplication over addition. 

P  =  2l + 2w

Subtract 2l from each side. 

P - 2l  =  2w

Divide each side by 2. 

(P - 2l) / 2  =  w

Problem 6 :

Solve for a :

Q  =  3a + 5ac

Solution : 

Q  =  3a + 5ac

Factor a out of 3a + 5ac. 

Q  =  a(3 + 5c)

Divide each side by (3 + 5c). 

Q / (3 + 5c)  =  a

Problem 7 : 

Solve for b₁ :

A  =  1/2 ⋅ h(b₁ + b₂)

Solution : 

A  =  1/2 ⋅ h(b₁ + b₂)

Multiply each side by 2/h. 

2A/h  =  b₁ + b₂

Subtract b₂ from each side. 

2A/h - b₂  =  b₁

Problem 8 : 

Solve for b :

a² + b²  =  c²

Solution : 

a² + b²  =  c²

Subtract a² from each side. 

b²  =  c² - a²

Take square root on each side. 

√b²  =  √(c² - a²)

b  =  √(c² - a²)

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