Math

QuestionSolve for xx in the equation: 13+4x=59\frac{1}{3}+\frac{4}{x}=\frac{5}{9}.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 13+4x=59\frac{1}{3}+\frac{4}{x}=\frac{5}{9}. . We need to solve for xx.

STEP 2

First, we need to get rid of the fractions. We can do this by multiplying every term by the least common multiple (LCM) of the denominators. The LCM of, xx, and9 is xx.
x1+x4x=x59x \cdot \frac{1}{} +x \cdot \frac{4}{x} =x \cdot \frac{5}{9}

STEP 3

implify each term.
x+12=53xx +12 = \frac{5}{3}x

STEP 4

To isolate xx, we need to get all terms with xx on one side of the equation and the constant on the other side. Subtract xx from both sides.
12=3xx12 = \frac{}{3}x - x

STEP 5

To simplify the right side of the equation, we need to find a common denominator for 53\frac{5}{3} and 11 (since xx is the same as x1\frac{x}{1}). The common denominator is3.
12=53x33x12 = \frac{5}{3}x - \frac{3}{3}x

STEP 6

Subtract the fractions on the right side of the equation.
12=23x12 = \frac{2}{3}x

STEP 7

To solve for xx, divide both sides of the equation by 23\frac{2}{3}.
x=1223x = \frac{12}{\frac{2}{3}}

STEP 8

implify the right side of the equation by multiplying 1212 by the reciprocal of 23\frac{2}{3}, which is 32\frac{3}{2}.
x=1232x =12 \cdot \frac{3}{2}

STEP 9

Calculate the value of xx.
x=18x =18The solution to the equation 3+4x=59\frac{}{3}+\frac{4}{x}=\frac{5}{9} is x=18x =18.

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