Algebra 1 Common Core Student Edition, Grade 8-9

G o t It? 1. a. Solve th e equ atio n 4 = 2m - 5n for m. W hat are th e values of m w h e n

n = - 2 , 0 , a n d 21

b. Reasoning Solve Problem 1 by substituting x = 3 a n d x = 6 into the

eq u a tio n lOx + 5y = 80 a n d th e n solving for y in each case. Do you

prefer this m eth o d or th e m eth o d show n in Problem 1? Explain.

Thi nk
How can you solve a
literal equation fo r a
variable?
When a literal equation
contains only variables,
tre at the variables you
are not solving fo r as
constants.

W hen you rewrite literal equations, you m ay have to divide by a variable or variable

expression. W hen you do so in this lesson, assum e th a t th e variable or variable

expression is n o t equal to zero because division by zero is n o t defined.

Problem 2 Rewriting a Literal Equation With Only Variables

What equation do you get when you solve ax — b x = c for x?

ax - bx= c

Distributive Property

Divide each side by a - b, where a - b + 0.

Simplify.

x( ci -

x[a

b)

b)

X =

a — b

c

& G o t It? 2. W hat equ atio n do you get w h en you solve — t = r + px for x?

A form ula is an equ atio n th at states a relationship am ong quantities. Form ulas are

special types of literal equations. Some com m on form ulas are given below. Notice

th at som e of th e form ulas use th e sam e variables, b u t th e definitions of th e variables

are different.

Formula Name Formula Definitions of Variables

P erim eter of a rectangle P = 2 € + 2w P = perimeter, € = length, w = width

C ircum ference of a circle C = 2irr C = circu m feren ce, r = radius

Area of a rectangle A = Vw A — area, € = length, w = width

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

Area of a circle A — 77T2 A — area, r = radius

D istance traveled d = rt d = distance, r = rate, t = tim e

Temperature

V

C = | ( F — 32) C = degrees Celsius, F = degrees F ahrenheit

J

110 Ch ap t er 2 So l v i n g Eq u a t i o n s