How to find out when an equation has no solution - SAT Math
Card 0 of 8
Find the solution to the following equation if x = 3:
y = (4x2 - 2)/(9 - x2)
Find the solution to the following equation if x = 3:
y = (4x2 - 2)/(9 - x2)
Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.
Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.
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I. x = 0
II. x = –1
III. x = 1
I. x = 0
II. x = –1
III. x = 1
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Compare your answer with the correct one above
A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.
A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.
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Solve:
Solve:
First, distribute, making sure to watch for negatives.
Combine like terms.
Subtract 7x from both sides.
Add 18 on both sides and be careful adding integers.
First, distribute, making sure to watch for negatives.
Combine like terms.
Subtract 7x from both sides.
Add 18 on both sides and be careful adding integers.
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Solve:
Solve:
First, distribute the 
to the terms inside the parentheses.
Add 6x to both sides.
This is false for any value of 
. Thus, there is no solution.
First, distribute the
Add 6x to both sides.
This is false for any value of
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Solve 
.
Solve
By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.
By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.
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, 
In the above graphic, approximately determine the x values where the graph is neither increasing or decreasing.
,
In the above graphic, approximately determine the x values where the graph is neither increasing or decreasing.
We need to find where the graph's slope is approximately zero. There is a straight line between the x values of 
, and 
. The other x values have a slope. So our final answer is 
.
We need to find where the graph's slope is approximately zero. There is a straight line between the x values of
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