Clear out the fractions by multiplying the ENTIRE equation by
the common denominator.
SPECIAL CASES
Sometimes when dealing with equations, all the variable cancel
out. When this happens we have a "special case". If the
expression we're left with is a true mathematical statement, our
solution is called the Identity Property which
means that there is an infinite number of solutions. The symbol
for infinity is . If the expression we're left with is a false
mathematical statement, there will be no solution. We indicate
this with the empty set symbol which is Ø.
Example 1
2x + 5 = 2x -3
To solve this equation, we need to
attempt to get the variables together on the same side.
2x + 5 - 2x = 2x -3 - 2x
When we subtract 2x from each side, all
variables are eliminated, leaving us with 5 = -3
5 = -3
We know this is a "special
case" since we have no variables. Since 5 is not
equal to -3, this is a false statement. Therefore there
are no solutions.
Ø
We write the empty set symbol for our
answer
Example 2
3 ( x + 1 ) - 5 = 3x -2
To solve this equation, we first remove
the parentheses by distributing.
3x + 3 - 5 = 3x - 2
We need to collect like terms (3 - 5 ) on
the left side
3x - 2 = 3x -2
To solve this equation, we need to
attempt to get the variables together on the same side.
3x - 2 - 3x = 3x -2 - 3x
We do this by subtracting 3x from each
side.
This gives us -2 = -2
-2 = -2
We know this is a "special
case" since we have no variables. Since -2 is equal
to -32, this is a true statement (the identity property).
Therefore there are infinite number of solutions.
We write the symbol for infinity for our
answer
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Algebrator can solve problems in all the following areas:
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solving linear, quadratic and many other equations
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solving a system of two and three linear equations
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. If the expression we're left with is a false
mathematical statement, there will be no solution. We indicate
this with the empty set symbol which is Ø. 
