Solving Equations for a Specific Variable

When solving for a specific variable, follow the same rules as when you are solving “regular” equations.Begin by identifying the variable you are

solving for.Then, SIMPLIFY the equation.

Remember – get rid of fractions, parentheses or like terms.

Next, ISOLATE that variable by “undoing” the operations around that variable.

Get all of the same variables on the same side of the equal sign.

Then, SOLVE for the variable.

Like this……

1. Solve for d:

2. Solve for n:

• Mark the variable you are solving for.

• “Undo” the operation that “connects” the ‘d’ to the other numbers or variables.• What operation connects

the 5 to the c2 and to the d?

• Multiplication – so what is it’s opposite?• Division• So divide both sides by

everything in front of the d.

25T c d25c25c

d25

T

c

23R m n23m23m

n23

R

m

If I’m solving for “w” I want all of my “w’s” on the LEFT side of the equal sign and all the “u’s” on the RIGHT…..so ISOLATE

Now SOLVE for “w”.

3. Solve for w:

5 5u w u w 5w5w

u4w5u5u 5u4w 4u4 4w u

If I’m solving for “u” I want all of my “u’s” on the LEFT side of the equal sign and all the “w’s” on the RIGHT…..so ISOLATE

Now SOLVE for “u”.

4. Solve for u:

5 5u w u w uu5ww 4u

w w4u 4w4 4u w

5. Solve for A: Simplify –

get rid of the parentheses then the fraction in this case.

Now mark your variable and ISOLATE.

And SOLVE for “A”

5( 8)7

B A

5

7A

40

7B (7) (7) (7)

7B 5A 404040

7 40B 5A55

A7 40

5

B

6. Solve for A:

7( 3)8

B A

7

8A

21

8B (8) (8) (8)

8B 7A 212121

8 21B 7A77

A8 21

7

B

7. Solve for c:

Simplify – get rid of the parentheses then the fraction in this case.

Now mark your variable and ISOLATE.

And SOLVE for “A”

1( )

2A h b c

1

2hb

1

2hcA(2) (2) (2)

2Ahb hchbhb

2A hb hchh

c2A hb

h h

8. Solve for b:

1( )

2A h b c

c 2 A bh

1

2hb

1

2hcA(2) (2) (2)

2Ahb hchchc

2A hc hbhh

b2A hc

h h

b2A c

h

1( )

2A h b c

9. Solve for h: 10. Solve for L:

AW

L

(2) (2)

2A ( )h b c( )b c( )b c

h2A

b c

( )L ( )L

AWLWW

LA

W