Math

QuestionResuelve la ecuación: 13+54x56=32x \frac{1}{3} + \frac{5}{4} x - \frac{5}{6} = \frac{3}{2} x

Studdy Solution

STEP 1

Assumptions1. The equation to solve is 13+54x56=3x\frac{1}{3}+\frac{5}{4} x-\frac{5}{6}=\frac{3}{} x . The variable to solve for is xx

STEP 2

First, we need to bring the terms involving xx to one side of the equation and the constant terms to the other side. This can be done by subtracting 54x\frac{5}{4}x from both sides of the equation.
156=2x54x\frac{1}{} - \frac{5}{6} = \frac{}{2}x - \frac{5}{4}x

STEP 3

Now, we simplify the right side of the equation by finding a common denominator for the fractions. The common denominator of2 and is.
1356=6x5x\frac{1}{3} - \frac{5}{6} = \frac{6}{}x - \frac{5}{}x

STEP 4

We simplify the right side of the equation by subtracting the fractions.
136=14x\frac{1}{3} - \frac{}{6} = \frac{1}{4}x

STEP 5

Next, we simplify the left side of the equation by finding a common denominator for the fractions. The common denominator of3 and is.
25=14x\frac{2}{} - \frac{5}{} = \frac{1}{4}x

STEP 6

We simplify the left side of the equation by subtracting the fractions.
36=14x-\frac{3}{6} = \frac{1}{4}x

STEP 7

We simplify the left side of the equation by reducing the fraction.
12=14x-\frac{1}{2} = \frac{1}{4}x

STEP 8

Finally, we solve for xx by multiplying both sides of the equation by4.
2=x-2 = xxx is equal to -2.

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