Question Find the values of $x$ that cannot be solutions to the equation $\frac{3 x}{3 x-8}-4=\frac{8}{7 x}$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $\frac{3x}{3x-8} - 4 = \frac{8}{7x}$ .
2. We need to find the value or values of $x$ that cannot be solutions to the equation.
3. These values are typically ones that make the denominator of any fraction in the equation equal to zero, as division by zero is undefined.

STEP 2

Identify the denominators in the given equation.
The denominators are $3x-8$ and $7x$ .

STEP 3

Set each denominator equal to zero to find the values of $x$ that would make the denominator undefined.
For $3x-8$ , we have: $3x - 8 = 0$
For $7x$ , we have: $7x = 0$

STEP 4

Solve the first equation $3x - 8 = 0$ for $x$ .
$3x = 8$
$x = \frac{8}{3}$

STEP 5

Solve the second equation $7x = 0$ for $x$ .
$x = \frac{0}{7}$
$x = 0$

STEP 6

Combine the results from STEP_4 and STEP_5 to list the excluded values.
The excluded values are $x = \frac{8}{3}$ and $x = 0$ .
The excluded value(s) is/are $\frac{8}{3}, 0$ .

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Question Find the values of $x$ that cannot be solutions to the equation $\frac{3 x}{3 x-8}-4=\frac{8}{7 x}$ .

Studdy Solution

STEP 1

STEP 2

Identify the denominators in the given equation.
The denominators are $3x-8$ and $7x$ .

STEP 3

Set each denominator equal to zero to find the values of $x$ that would make the denominator undefined.
For $3x-8$ , we have: $3x - 8 = 0$
For $7x$ , we have: $7x = 0$

STEP 4

Solve the first equation $3x - 8 = 0$ for $x$ .
$3x = 8$
$x = \frac{8}{3}$

STEP 5

Solve the second equation $7x = 0$ for $x$ .
$x = \frac{0}{7}$
$x = 0$

STEP 6

Combine the results from STEP_4 and STEP_5 to list the excluded values.
The excluded values are $x = \frac{8}{3}$ and $x = 0$ .
The excluded value(s) is/are $\frac{8}{3}, 0$ .

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Question Find the values of xxx that cannot be solutions to the equation 3x3x−8−4=87x\frac{3 x}{3 x-8}-4=\frac{8}{7 x}3x−83x​−4=7x8​.

Studdy Solution

STEP 1

STEP 2

Identify the denominators in the given equation.The denominators are 3x−83x-83x−8 and 7x7x7x.

STEP 3

Set each denominator equal to zero to find the values of xxx that would make the denominator undefined.For 3x−83x-83x−8, we have: 3x−8=03x - 8 = 03x−8=0For 7x7x7x, we have: 7x=07x = 07x=0

STEP 4

Solve the first equation 3x−8=03x - 8 = 03x−8=0 for xxx.3x=83x = 83x=8x=83x = \frac{8}{3}x=38​

STEP 5

Solve the second equation 7x=07x = 07x=0 for xxx.x=07x = \frac{0}{7}x=70​x=0x = 0x=0

STEP 6

Combine the results from STEP_4 and STEP_5 to list the excluded values.The excluded values are x=83x = \frac{8}{3}x=38​ and x=0x = 0x=0.The excluded value(s) is/are 83,0\frac{8}{3}, 038​,0.

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Question Find the values of $x$ that cannot be solutions to the equation $\frac{3 x}{3 x-8}-4=\frac{8}{7 x}$ .

Identify the denominators in the given equation.
The denominators are $3x-8$ and $7x$ .

Set each denominator equal to zero to find the values of $x$ that would make the denominator undefined.
For $3x-8$ , we have: $3x - 8 = 0$
For $7x$ , we have: $7x = 0$

Solve the first equation $3x - 8 = 0$ for $x$ .
$3x = 8$
$x = \frac{8}{3}$

Solve the second equation $7x = 0$ for $x$ .
$x = \frac{0}{7}$
$x = 0$

Combine the results from STEP_4 and STEP_5 to list the excluded values.
The excluded values are $x = \frac{8}{3}$ and $x = 0$ .
The excluded value(s) is/are $\frac{8}{3}, 0$ .