QuestionSolve $\frac{7}{x}=\frac{2}{3 x}-10$ for $x$ . What is $x$ ?

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{7}{x}=\frac{}{3 x}-10$ . We are solving for x

STEP 2

First, we need to get rid of the fractions in the equation. We can do this by multiplying every term by $x$ .
$x \cdot \frac{7}{x} = x \cdot \frac{2}{ x} - x \cdot10$

STEP 3

implify the equation.
$7 = \frac{2}{3} -10x$

STEP 4

Next, we want to isolate the term with $x$ . We can do this by moving $\frac{2}{3}$ to the left side of the equation.
$7 - \frac{2}{3} = -10x$

STEP 5

implify the left side of the equation.
$\frac{19}{3} = -10x$

STEP 6

Finally, we can solve for $x$ by dividing both sides of the equation by $-10$ .
$x = \frac{\frac{19}{3}}{-10}$

STEP 7

implify the right side of the equation.
$x = -\frac{19}{30}$ So, the solution to the equation $\frac{7}{x}=\frac{2}{3 x}-10$ is $x = -\frac{19}{30}$ .

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QuestionSolve $\frac{7}{x}=\frac{2}{3 x}-10$ for $x$ . What is $x$ ?

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{7}{x}=\frac{}{3 x}-10$ . We are solving for x

STEP 2

First, we need to get rid of the fractions in the equation. We can do this by multiplying every term by $x$ .
$x \cdot \frac{7}{x} = x \cdot \frac{2}{ x} - x \cdot10$

STEP 3

implify the equation.
$7 = \frac{2}{3} -10x$

STEP 4

Next, we want to isolate the term with $x$ . We can do this by moving $\frac{2}{3}$ to the left side of the equation.
$7 - \frac{2}{3} = -10x$

STEP 5

implify the left side of the equation.
$\frac{19}{3} = -10x$

STEP 6

Finally, we can solve for $x$ by dividing both sides of the equation by $-10$ .
$x = \frac{\frac{19}{3}}{-10}$

STEP 7

implify the right side of the equation.
$x = -\frac{19}{30}$ So, the solution to the equation $\frac{7}{x}=\frac{2}{3 x}-10$ is $x = -\frac{19}{30}$ .

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QuestionSolve 7x=23x−10\frac{7}{x}=\frac{2}{3 x}-10x7​=3x2​−10 for xxx. What is xxx?

Studdy Solution

STEP 1

Assumptions1. The equation is 7x=3x−10\frac{7}{x}=\frac{}{3 x}-10x7​=3x​−10 . We are solving for x

STEP 2

First, we need to get rid of the fractions in the equation. We can do this by multiplying every term by xxx.x⋅7x=x⋅2x−x⋅10x \cdot \frac{7}{x} = x \cdot \frac{2}{ x} - x \cdot10x⋅x7​=x⋅x2​−x⋅10

STEP 3

implify the equation.7=23−10x7 = \frac{2}{3} -10x7=32​−10x

STEP 4

Next, we want to isolate the term with xxx. We can do this by moving 23\frac{2}{3}32​ to the left side of the equation.7−23=−10x7 - \frac{2}{3} = -10x7−32​=−10x

STEP 5

implify the left side of the equation.193=−10x\frac{19}{3} = -10x319​=−10x

STEP 6

Finally, we can solve for xxx by dividing both sides of the equation by −10-10−10.x=193−10x = \frac{\frac{19}{3}}{-10}x=−10319​​

STEP 7

implify the right side of the equation.x=−1930x = -\frac{19}{30}x=−3019​So, the solution to the equation 7x=23x−10\frac{7}{x}=\frac{2}{3 x}-10x7​=3x2​−10 is x=−1930x = -\frac{19}{30}x=−3019​.

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QuestionSolve $\frac{7}{x}=\frac{2}{3 x}-10$ for $x$ . What is $x$ ?

Assumptions1. The equation is $\frac{7}{x}=\frac{}{3 x}-10$ . We are solving for x

First, we need to get rid of the fractions in the equation. We can do this by multiplying every term by $x$ .
$x \cdot \frac{7}{x} = x \cdot \frac{2}{ x} - x \cdot10$

implify the equation.
$7 = \frac{2}{3} -10x$

Next, we want to isolate the term with $x$ . We can do this by moving $\frac{2}{3}$ to the left side of the equation.
$7 - \frac{2}{3} = -10x$

implify the left side of the equation.
$\frac{19}{3} = -10x$

Finally, we can solve for $x$ by dividing both sides of the equation by $-10$ .
$x = \frac{\frac{19}{3}}{-10}$

implify the right side of the equation.
$x = -\frac{19}{30}$ So, the solution to the equation $\frac{7}{x}=\frac{2}{3 x}-10$ is $x = -\frac{19}{30}$ .