SOLVING LITERAL EQUATIONS

What is a literal equation?

A literal equation is an equation that consists primarily of letters.

Formulas are an example of literal equations.

Each variable in the equation "literally" represents an important part of the whole relationship expressed by the equation.

How to solve a literal equations ?

Step 1 :

Identify the variable that we need to isolate.

Step 2 :

Using inverse operations, we have remove the remaining terms all around the variable that we have targeted.

Step 3 :

We apply all the rules of algebra while solving equations.

Solve A = (a + b)/2 for b

Solve the following :

Example 1 :

Solve V = lwh for w

Solution :

Given,

V = lwh

Solving for w.

Divide by lh on both sides,

V/lh = w

w = V/lh

So, the solution of w is V/lh.

Example 2 :

Solve m = (y2 - y1)/(x- x1) for y2

Solution :

Given,

m = (y- y1)/(x- x1)

Solving for y2.

Multiply by (x- x1) on both sides,

m(x- x1) = y- y1

mx- mx1 = y- y1

Add y1 on both sides,

mx- mx1 + y1 = y2

y2 = mx- mx1 + y1

So, the solution of y2 is mx- mx1 + y1.

Example 3 :

Solve ax + by = c for y

Solution :

Given,

 ax + by = c

Solving for y.

Subtract ax on both sides,

by = c - ax

Divide by b on both sides,

y = (c - ax)/b

So, the solution of y is (c - ax)/b.

Example 4 :

Solve A = (a + b + c + d)/4 for c

Solution :

Given,

A = (a + b + c + d)/4

Solving for c.

Multiply by 4 on both sides,

4A = a + b + c + d

Along with c, a, b and d are added. So, subtract a, b and d on both sides.

4A - a - b - d = c

c = 4A - a - b - d

So, the solution of c is 4A - a - b - d.

Example 5 :

Solve S = 2(lw + lh + wh) for w.

Solution :

Given,

S = 2(lw + lh + wh)

S = 2lw + 2lh + 2wh

By combining like terms,

S = 2lw + 2wh + 2lh

S = 2w(l + h) + 2lh

Solving for w.

Subtract by 2lh on both sides,

S - 2lh = 2w(l + h)

Divide by 2(l + h) both sides,

(S - 2lh)/[2(l + h)] = w

w = (S - 2lh)/(2l + 2h)

So, the solution of c is (S - 2lh)/(2l + 2h).

Example 6 :

Solve P = 2(l + w) for l

Solution :

Given,

P = 2(l + w)

P = 2l + 2w

Solving for l.

Subtract 2w on both sides,

P - 2w = 2l

Divide by 2 on both sides,

(P - 2w)/2 = l

So, the solution of l is (P - 2w)/2.

Example 7 :

Solve d = c/π for π

Solution :

Given,

d = c/π

πd = c

Solving for π.

Divide by d on both sides,

π = c/d

Example 8 :

Solve 5t - 2r = 25 for t

Solution :

Given,

5t - 2r = 25

Solving for t.

Add 2r on both sides, 

5t = 25 + 2r

Divide by 5 on both sides, 

t = 25/5 + 2/5r

t = 5 + 2/5r

Example 9 :

Solve S = R - rR for R.

Solution :

Given,

S = R - rR

S = R(1 - r)

Solving for R.

Divide by (1 - r) on both sides,

S/(1 - r) = R

Example 10 :

Solve V = 1/3πh2(3r - h) for r

Solution :

Given,

V = 1/3πh2(3r - h)

By using the distributive property,

V = 3/3πh2r - 1/3πh3

V = πh2r - πh3/3

By taking the least common multiple,

V = (3πh2r - πh3)/3

Solving for r.

Multiply by 3 on both sides,

3V = 3πh2r - πh3

Add πh3 on both sides,

3V + πh3πh2r

Divide by 3πh2 on both sides,

(3V + πh3)/3πhr

Example 11 :

Solve A = 1/2nal for n

Solution :

Given,

 A = 1/2nal

Solving for n.

Multiply by 2 on both sides,

2A = nal

Divide by al on both sides,

2A/al = n

Example 12 :

Solve (p1v1)/T1 = (p2v2)/T2 for T1

Solution :

Given,

(p1v1)/T= (p2v2)/T2

Solving for T1.

Multiply by T1 on both sides,

p1v= T1(p2v2)/T2

Multiply by T2 on both sides,

T2(p1v1) = T1(p2v2)

Divide by p2von both sides,

T2(p1v1)/(p2v2) = T1

Example 13 :

Solve F = (gm1m2)/d2 for g

Solution :

Given,

F = (gm1m2)/d2

Solving for g.

Multiply by d2 on both sides,

Fd2 = gm1m2

Divide by m1m2 on both sides,

Fd2/m1m= g

Example 14 :

Solve (12ds)/w = CD for w

Solution :

Given,

(12ds)/w = CD

Solving for w.

Multiply by w on both sides,

12ds = wCD

Divide by CD on both sides,

12ds/CD = w

Example 15 :

Solve A = 1/2bh for b

Solution :

Given,

A = 1/2bh

Solving for b.

Multiply by 2 on both sides,

2A = bh

Divide by h on both sides,

2A/h = b

Recent Articles

  1. Factoring Exponential Expression Using Algebraic Identities Worksheet

    Mar 14, 24 10:44 PM

    Factoring Exponential Expression Using Algebraic Identities Worksheet

    Read More

  2. Positive and Negative Numbers Connecting in Real Life Worksheet

    Mar 14, 24 10:12 AM

    Positive and Negative Numbers Connecting in Real Life Worksheet

    Read More

  3. Positive and Negative Numbers Connecting in Real Life

    Mar 14, 24 09:52 AM

    Positive and Negative Numbers Connecting in Real Life

    Read More