QuestionSolve for $x$ in the equation $\frac{7}{2} x=\frac{4}{3} x-\frac{1}{6}$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $\frac{7}{}x = \frac{4}{3}x - \frac{1}{6}$ . We need to solve for $x$

STEP 2

First, we need to get all terms involving $x$ on one side of the equation. We can do this by subtracting $\frac{4}{}x$ from both sides of the equation.
$\frac{7}{2}x - \frac{4}{}x = \frac{4}{}x - \frac{1}{6} - \frac{4}{}x$

STEP 3

implify the left side of the equation.
$\left(\frac{7}{2} - \frac{}{3}\right)x = -\frac{1}{6}$

STEP 4

To subtract the fractions, we need to find a common denominator. The least common multiple of2 and3 is6.
$\left(\frac{21}{6} - \frac{8}{6}\right)x = -\frac{1}{6}$

STEP 5

Subtract the fractions on the left side of the equation.
$\frac{13}{}x = -\frac{1}{}$

STEP 6

To solve for $x$ , we need to divide both sides of the equation by $\frac{13}{6}$ .
$x = \frac{-\frac{1}{6}}{\frac{13}{6}}$

STEP 7

implify the right side of the equation. This is a complex fraction, so we can simplify it by multiplying the numerator and the denominator by the reciprocal of the denominator.
$x = -\frac{1}{6} \times \frac{6}{13}$

STEP 8

implify the multiplication.
$x = -\frac{1}{13}$ So, the solution to the equation is $x = -\frac{1}{13}$ .

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QuestionSolve for $x$ in the equation $\frac{7}{2} x=\frac{4}{3} x-\frac{1}{6}$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $\frac{7}{}x = \frac{4}{3}x - \frac{1}{6}$ . We need to solve for $x$

STEP 2

First, we need to get all terms involving $x$ on one side of the equation. We can do this by subtracting $\frac{4}{}x$ from both sides of the equation.
$\frac{7}{2}x - \frac{4}{}x = \frac{4}{}x - \frac{1}{6} - \frac{4}{}x$

STEP 3

implify the left side of the equation.
$\left(\frac{7}{2} - \frac{}{3}\right)x = -\frac{1}{6}$

STEP 4

To subtract the fractions, we need to find a common denominator. The least common multiple of2 and3 is6.
$\left(\frac{21}{6} - \frac{8}{6}\right)x = -\frac{1}{6}$

STEP 5

Subtract the fractions on the left side of the equation.
$\frac{13}{}x = -\frac{1}{}$

STEP 6

To solve for $x$ , we need to divide both sides of the equation by $\frac{13}{6}$ .
$x = \frac{-\frac{1}{6}}{\frac{13}{6}}$

STEP 7

implify the right side of the equation. This is a complex fraction, so we can simplify it by multiplying the numerator and the denominator by the reciprocal of the denominator.
$x = -\frac{1}{6} \times \frac{6}{13}$

STEP 8

implify the multiplication.
$x = -\frac{1}{13}$ So, the solution to the equation is $x = -\frac{1}{13}$ .

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QuestionSolve for xxx in the equation 72x=43x−16\frac{7}{2} x=\frac{4}{3} x-\frac{1}{6}27​x=34​x−61​.

Studdy Solution

STEP 1

Assumptions1. The given equation is 7x=43x−16\frac{7}{}x = \frac{4}{3}x - \frac{1}{6}7​x=34​x−61​ . We need to solve for xxx

STEP 2

First, we need to get all terms involving xxx on one side of the equation. We can do this by subtracting 4x\frac{4}{}x4​x from both sides of the equation.72x−4x=4x−16−4x\frac{7}{2}x - \frac{4}{}x = \frac{4}{}x - \frac{1}{6} - \frac{4}{}x27​x−4​x=4​x−61​−4​x

STEP 3

implify the left side of the equation.(72−3)x=−16\left(\frac{7}{2} - \frac{}{3}\right)x = -\frac{1}{6}(27​−3​)x=−61​

STEP 4

To subtract the fractions, we need to find a common denominator. The least common multiple of2 and3 is6.(216−86)x=−16\left(\frac{21}{6} - \frac{8}{6}\right)x = -\frac{1}{6}(621​−68​)x=−61​

STEP 5

Subtract the fractions on the left side of the equation.13x=−1\frac{13}{}x = -\frac{1}{}13​x=−1​

STEP 6

To solve for xxx, we need to divide both sides of the equation by 136\frac{13}{6}613​.x=−16136x = \frac{-\frac{1}{6}}{\frac{13}{6}}x=613​−61​​

STEP 7

implify the right side of the equation. This is a complex fraction, so we can simplify it by multiplying the numerator and the denominator by the reciprocal of the denominator.x=−16×613x = -\frac{1}{6} \times \frac{6}{13}x=−61​×136​

STEP 8

implify the multiplication.x=−113x = -\frac{1}{13}x=−131​So, the solution to the equation is x=−113x = -\frac{1}{13}x=−131​.

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QuestionSolve for $x$ in the equation $\frac{7}{2} x=\frac{4}{3} x-\frac{1}{6}$ .

Assumptions1. The given equation is $\frac{7}{}x = \frac{4}{3}x - \frac{1}{6}$ . We need to solve for $x$

First, we need to get all terms involving $x$ on one side of the equation. We can do this by subtracting $\frac{4}{}x$ from both sides of the equation.
$\frac{7}{2}x - \frac{4}{}x = \frac{4}{}x - \frac{1}{6} - \frac{4}{}x$

implify the left side of the equation.
$\left(\frac{7}{2} - \frac{}{3}\right)x = -\frac{1}{6}$

To subtract the fractions, we need to find a common denominator. The least common multiple of2 and3 is6.
$\left(\frac{21}{6} - \frac{8}{6}\right)x = -\frac{1}{6}$

Subtract the fractions on the left side of the equation.
$\frac{13}{}x = -\frac{1}{}$

To solve for $x$ , we need to divide both sides of the equation by $\frac{13}{6}$ .
$x = \frac{-\frac{1}{6}}{\frac{13}{6}}$

implify the right side of the equation. This is a complex fraction, so we can simplify it by multiplying the numerator and the denominator by the reciprocal of the denominator.
$x = -\frac{1}{6} \times \frac{6}{13}$

implify the multiplication.
$x = -\frac{1}{13}$ So, the solution to the equation is $x = -\frac{1}{13}$ .