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QuestionSolve the equation: 56x−x=910x−5\frac{5}{6} x - x = \frac{9}{10} x - 5.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 56x−x=910x−5\frac{5}{6} x-x=\frac{9}{10} x-5 . We are required to solve for xx

STEP 2

First, we simplify the left side of the equation. We can do this by finding a common denominator for 56x\frac{5}{6} x and xx.
56x−x=56x−66x\frac{5}{6} x - x = \frac{5}{6} x - \frac{6}{6} x

STEP 3

Subtract the fractions on the left side of the equation.
56x−66x=−16x\frac{5}{6} x - \frac{6}{6} x = -\frac{1}{6} x

STEP 4

Now, we simplify the right side of the equation. We can do this by moving the constant term to the left side of the equation.
−16x+=910x-\frac{1}{6} x + = \frac{9}{10} x

STEP 5

Next, we move the term containing xx on the right side of the equation to the left side.
−1x−910x=−5-\frac{1}{} x - \frac{9}{10} x = -5

STEP 6

To subtract the fractions, we need to find a common denominator for 16x\frac{1}{6} x and 910x\frac{9}{10} x. The common denominator is30.
−530x−2730x=−5-\frac{5}{30} x - \frac{27}{30} x = -5

STEP 7

Subtract the fractions on the left side of the equation.
−3230x=−5-\frac{32}{30} x = -5

STEP 8

implify the fraction on the left side of the equation.
−1615x=−5-\frac{16}{15} x = -5

STEP 9

To solve for xx, we divide both sides of the equation by −1615-\frac{16}{15}.
x=−5−1615x = \frac{-5}{-\frac{16}{15}}

STEP 10

implify the right side of the equation to find the value of xx.
x=−5−1615=7516x = \frac{-5}{-\frac{16}{15}} = \frac{75}{16}So, the solution to the equation is x=7516x = \frac{75}{16}.

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