Linear Equations
Now we can use the tools we have developed to solve equations. Up to now, we have rewritten expressions and added fractions. This chapter is mostly concerned with linear equations. In a linear equation, the variables are raised to the first power—there are no variables in denominators, no variables to any power (other than one), and no variables under root signs.
In solving for linear
equations, there will be an unknown, usually only one but possibly several.
What is meant by ‘‘solve for x’’ is to isolate x on one side of the equation
and to move everything else on the other side. Usually, although not always,
the last line is the sentence.
‘‘x = (number)’’
Where the number satisfies the
original equation. That is, when the number is substituted for x, the equation
is true.
In the equation 3x + 7 =
1; x = –2 is the solution because 3(–2) + 7 = 1 is a true statement. For any
other number, the statement would be false. Fo instance, if we were to say that
x = 4, the sentence would be 3(4) + 7 = 1, which is false.
Not every equation will
have a solution. For example, x + 3 = x + 10 has no solution. Why not? There is
no number that can be added to three and be the same quantity as when it is
added to 10. If you were to try to solve for x, you would end up with the false
statement 3 = 10.
In order to solve equations and to verify solutions, you must know the order of operations. For example, in the formula
What is done first? Second? Third?
A pneumonic for remembering operation
order is ‘‘Please excuse my dear Aunt Sally.’’
P – parentheses first
E – exponents (and roots) second
M – multiplication third
D – division third (multiplication and division should be
done together,
working from left to right)
A – addition fourth
S – subtraction fourth (addition and subtraction should be
done together,
working from left to right)
When working with fractions, think of
numerators and denominators as being in parentheses.
Examples
Practice
Solutions
“Sumber
Informasi”
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