SOLVING LITERAL EQUATIONS AND

FORMULAS

Lesson 2-5

A _______________ _______________ is an equation that involves two or more variables.

literal equation

Rewriting a Literal Equation:

A. –2x + 5y = 12 Solve for y.

_________________________________ Add 2x to each side to “move” the x-term (You are trying to get “y” by itself.)

_________________________________ Simplify

_________________________________ Divide by 5

_________________________________ Simplify

– 2x + 2x + 5y = 12 + 2x

5y = 12 + 2x

Note: I work most of my literal equations vertically because often there are no like terms to line up when adding or subtracting.

B. a – 2b = –10 Solve for b.

________________________________ Subtract a from each

side.

________________________________ Simplify

________________________________ Divide by –2

________________________________ Simplify

a – 2b – a = – 10 – a

– 2b = – 10 – a

Factor each of the following expressions:

C. –3x – 9 = ____ (x + 3)

D. 2xy + 6y = ____ (x + 3)

E. 9x – 18 = ____ (x – 2)

F. ax – bx = ___ ( ____ – ____ )

– 3

2y

2y

x a b

This is like doing the distributive property

in reverse

Rewriting a Literal Equation with only (mostly) Variables

G. mx + 2nx = p Solve for x.

______________________________________ Use the distributive property to factor out the x

_______________________________________ Divide both sides by ________.

_______________________________________ Simplify

x(m + 2n) = p

m + 2n

Rewriting Formulas

A formula is an equation that states a __________________ among quantities. Formulas are special types of ______________ _____________________

Some formulas you should know are on the table below:

relationship

literal equations

Formula Name Formula Definitions of Variables

Perimeter of a rectangle P = 2l + 2w P = perimeter, l = length, w = width

Circumference of a circle C = 2πr C = circumference, r = radius

Area of a rectangle A = lw A = area, l = length, w = width

Area of a triangle A = ½ bh A = area, b = base, h = height

Area of a circle A = πr2 A = area, r = radius

Distance traveled d = rt D = distance, r = rate, t = time

Temperature C = degrees Celsius, F = degrees Fahrenheit

9

5

I. Josh is planting a rectangular garden. The perimeter of the garden is 120 yd., and the width is 20 yd. What is the length of the garden?

Solve the formula for length: Substitute the value of P and w:

__________________________

____________________________

__________________________

____________________________

__________________________

____________________________

__________________________

__________________________

P = 2l + 2w

P – 2w = 2l + 2w – 2w

P – 2w = 2l

40 = l