Algebra 1 Notes SOL A.4 Solving for a Variable
Mrs. Grieser
Name: ____________________________________________ Date: _____________Block: _________
Solving for a Variable
Literal Equation
Formula

An equation that uses letters to replace coefficients.

Models patterns found in certain equations

Example: Ax + By = C; in this equation, A and B represent constant
coefficients and are not variables.

An equation that relates two or more quantities.
5
Example: C  F  32 (Fahrenheit to Celsius conversion)
9

Solving for a Variable
 Use the properties of equality to solve a literal equation or formula for a certain variable.

Exactly like solving an equation with numbers, only manipulate variables instead of
numbers.

Example: Solve 4x + 2y = 8 for y
o Means: change the equation to y = ...
o Isolate y, just like you would when solving any equation:

Subtract 4x from both sides: 2y = -4x + 8

Divide both sides by 2:
2 y  4x  8

=
2
2
y = -2x + 4
Important! Solving for y has a special name: Putting an equation in function form
Examples:
1) Solve literal equation ax + b = c for x.
3) Solve A 
1
bh for h (area of
2
2) Write 4x + 2y = 8 in function form
(solve for y)
4) Write a formula for converting Celsius to
Fahrenheit.
a triangle).
C
5
F  32
9
You try (first row: put in function form; otherwise solve as directed):
a) 2x + y = 7
b) 12 = 9x + 3y
c) 9x – 5y = 30
d) Solve for x: ax  b  c
e) Solve for x: c 
g) Solve for w: V  lwh
h) Solve for h: S  2B  Ph
xa
b
f) Solve for x:
x
a

i) Solve for h: A 
b
c
1
2
h(b1  b2 )