Transcript 1.4 Solving Linear Equations

1.4 SOLVING LINEAR EQUATIONS

A __________ ____________ in one variable x is an
equation that can be written in the form
ax  b  0
where a and b are real numbers, and a ≠ 0.
SOLVING AN EQUATION
Solving an equation in x involves determining all
values of x that result in a _________statement
when substituted into the equation.
 Such values are called ____________, or ________
of the equation.

EQUIVALENT EQUATIONS


Equivalent equations are two or more equations
that have the same ____________________.
For example,
, and x  3
are equivalent equations because the solution set
for each is {-3}.
4x 12  0 , 4 x  12
PROPERTIES OF EQUALITY

The addition property of equality:


The same real number or algebraic expression may
be added to both sides of an equation without
changing the equation’s _____________ _______.
The multiplicative property of equality:

The same nonzero real number may multiply both
sides of an equation without changing the equation’s
______________ _______.
USING PROPERTIES OF EQUALITY TO
SOLVE LINEAR EQUATIONS

x 3  8
add 3 to both sides
x 3
x

8
6x  30
divide both sides by 6 (or multiply by ____ )
6x  30
x
EXAMPLE 1:

Solve and check

4x  5  29
STEPS FOR SOLVING A LINEAR EQUATION
_____________ the algebraic expression on each
side by removing grouping symbols and
combining like terms.
 Collect all the _________ terms on one side and
all the numbers, or constant terms, on the other
side.
 Isolate the __________ and solve.
 Check the proposed solution in the ___________
equation.

EXAMPLE 2:

Solve and Check

2x 12  x  6x  4  5x
EXAMPLE 3:

Solve and Check:

2x  3 17  13  3x  2
EXAMPLE 4:

Solve and check:

x5 x 3 5


7
4
14
TYPES OF EQUATIONS
An equation that is true for all real numbers for
which both sides are defined is called an
__________.
 An equation that is not an identity, but that is
true for at least one real number, is called a
_______________ equation.
 An ________________ equation is an equation that
is not true for even one real number.

EXAMPLE 5:

Solve and determine whether the equation is an
identity, a conditional equation or an inconsistent
equation

4x  7  4x 1  3
EXAMPLE 6:

Solve and determine whether the equation is an
identity, a conditional equation, or an
inconsistent equation.

7 x  9  9x  1  2 x
Example 7:

The formula
N = 0.12x + 0.4
models the of new motorcycles sold in the United
States, N, in millions, x years after 1998. When
will new motorcycle sales reach 1.6 million?
Homework:

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