Chapter 7 linear equaTionS 187

by 5, so to move 5 across the equal sign, we need to “unmultiply” the 5. That is,
divide both sides of the equation by 5 (equivalently, multiply each side of the
equation by^15 ). In the equation 5 + x = 10, to move 5 across the equal sign by
“unadding” 5. That is, subtract 5 from both sides of the equation (equivalently,
add –5 to both sides of the equation).
In short, what is added must be subtracted; what is subtracted must be
added; what is multiplied must be divided; and what is divided must be multi-
plied. There are other operation pairs (an operation and its inverse); some will
be discussed later.
In much of this book, when the coefficient of x (the number multiplying x)
is an integer, both sides of the equation will be divided by that integer. And
when the coefficient is a fraction, both sides of the equation will be multiplied
by the reciprocal of that fraction.

EXAMPLES

Solve the equation.

5 x = 2

5 x = 2 Divide both sides by 5 or multiply both sides by 51.

5

5

2

5

2

5

x

x

=

=

Solve the equation.

2

3

x= (^6)
We want to isolate x, so we eliminate the coefficient of x,^23 , by dividing each
side of the equation by this number. Dividing each side by^23 is the same as
multiplying each side by 23.
3
2
2
3
3
2
6
9
⋅=⋅

x
x
Solve the equation.
−= 31 x 8
−=
−
−

−
=−
318
3
3
18
3
6
x
x
x
EXAMPLES
Solve the equation.
5
EXAMPLES
Solve the equation.