1.4 s olving l inear e quations a __________ ____________ in one variable x is an equation that can...
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1.4 SOLVING LINEAR EQUATIONS
A __________ ____________ in one variable x is an equation that can be written in the form
where a and b are real numbers, and a ≠ 0.
0bax
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 are equivalent equations because the solution
set for each is {-3}.
0124 x 124 x 3x
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
add 3 to both sides
divide both sides by 6 (or multiply by ____ )
83x
3x 8x
306 x
x
306 x
EXAMPLE 1:
Solve and check 2954 x
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 xxxx 546122
EXAMPLE 3:
Solve and Check: 23131732 xx
EXAMPLE 4:
Solve and check:
14
5
4
3
7
5
xx
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 31474 xx
EXAMPLE 6:
Solve and determine whether the equation is an identity, a conditional equation, or an inconsistent equation. xxx 21997
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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