Question
Variable Expressions in Denominators Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
What is the undefined value for 22=4+5x9x−6
?
Write your answer in reduced fraction form, if applicable.
(1 point)
The undefined value is
.
Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
What is the undefined value for 22=4+5x9x−6
?
Write your answer in reduced fraction form, if applicable.
(1 point)
The undefined value is
.
Answers
GPT-4o mini
To find the undefined value in the expression \( 22 = 4 + 5x \cdot 9x - 6 \), we first need to simplify and analyze the expression on the right side.
Starting with the equation:
\[
22 = 4 + 5x \cdot 9x - 6
\]
First, simplify the right side:
\[
5x \cdot 9x = 45x^2
\]
Now, substitute that back into the equation:
\[
22 = 4 + 45x^2 - 6
\]
Combine like terms:
\[
22 = (4 - 6) + 45x^2
\]
\[
22 = -2 + 45x^2
\]
Next, add 2 to both sides of the equation:
\[
22 + 2 = 45x^2
\]
\[
24 = 45x^2
\]
Now, solve for \( x^2 \):
\[
x^2 = \frac{24}{45}
\]
Reduce the fraction:
\[
x^2 = \frac{8}{15}
\]
Now, to find the undefined values, we need to determine when \( 45x^2 - 24 = 0 \):
\[
45x^2 - 24 = 0
\]
\[
45x^2 = 24
\]
\[
x^2 = \frac{24}{45} = \frac{8}{15}
\]
Now, to find \( x \), we take the square root of both sides:
\[
x = \pm \sqrt{\frac{8}{15}} = \pm \frac{2\sqrt{2}}{\sqrt{15}}
\]
The undefined value for the original expression occurs when the denominator equals zero. However, in your question, it appears we are meant to identify a certain value related to this equation.
Since the simplified expression doesn’t yield a specific denominator to evaluate for undefined values, the expected result regarding undefined values typically pertains to fractions where the denominator would equal zero. Given that \( 45x^2 \) can not yield 0 through any real number without specifically being expressed by values leading the right-hand portion to be undefined.
Thus, to answer your question based on standard protocol:
Given that the derived fractions \( \frac{8}{15} \) lead us without a defined expression, it seems traditional learning arrives at no defined real number capture within. Thus without further expression variations specified, we should denote:
The undefined value is \( \frac{8}{15} \).
Starting with the equation:
\[
22 = 4 + 5x \cdot 9x - 6
\]
First, simplify the right side:
\[
5x \cdot 9x = 45x^2
\]
Now, substitute that back into the equation:
\[
22 = 4 + 45x^2 - 6
\]
Combine like terms:
\[
22 = (4 - 6) + 45x^2
\]
\[
22 = -2 + 45x^2
\]
Next, add 2 to both sides of the equation:
\[
22 + 2 = 45x^2
\]
\[
24 = 45x^2
\]
Now, solve for \( x^2 \):
\[
x^2 = \frac{24}{45}
\]
Reduce the fraction:
\[
x^2 = \frac{8}{15}
\]
Now, to find the undefined values, we need to determine when \( 45x^2 - 24 = 0 \):
\[
45x^2 - 24 = 0
\]
\[
45x^2 = 24
\]
\[
x^2 = \frac{24}{45} = \frac{8}{15}
\]
Now, to find \( x \), we take the square root of both sides:
\[
x = \pm \sqrt{\frac{8}{15}} = \pm \frac{2\sqrt{2}}{\sqrt{15}}
\]
The undefined value for the original expression occurs when the denominator equals zero. However, in your question, it appears we are meant to identify a certain value related to this equation.
Since the simplified expression doesn’t yield a specific denominator to evaluate for undefined values, the expected result regarding undefined values typically pertains to fractions where the denominator would equal zero. Given that \( 45x^2 \) can not yield 0 through any real number without specifically being expressed by values leading the right-hand portion to be undefined.
Thus, to answer your question based on standard protocol:
Given that the derived fractions \( \frac{8}{15} \) lead us without a defined expression, it seems traditional learning arrives at no defined real number capture within. Thus without further expression variations specified, we should denote:
The undefined value is \( \frac{8}{15} \).