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QuestionSolve for xx in the equation: 13x+3=143\frac{1}{3} x + 3 = \frac{14}{3}.

Studdy Solution

STEP 1

Assumptions1. The equation is 13x+3=143\frac{1}{3} x+3=\frac{14}{3}

STEP 2

The first step to solve this equation is to isolate the term with the variable on one side of the equation. We can do this by subtracting from both sides of the equation.
1x+−=14−\frac{1}{} x+-=\frac{14}{}-

STEP 3

implify both sides of the equation.
13x=143−3\frac{1}{3} x=\frac{14}{3}-3

STEP 4

Convert3 to a fraction with3 as the denominator to make the subtraction easier.
3=933=\frac{9}{3}So, the equation becomes13x=143−93\frac{1}{3} x=\frac{14}{3}-\frac{9}{3}

STEP 5

Subtract the fractions on the right side of the equation.
13x=143−93=53\frac{1}{3} x=\frac{14}{3}-\frac{9}{3}=\frac{5}{3}

STEP 6

To isolate x, we need to get rid of the fraction 13\frac{1}{3} that is multiplying x. We can do this by multiplying both sides of the equation by the reciprocal of 13\frac{1}{3}, which is3.
3×13x=3×533 \times \frac{1}{3} x=3 \times \frac{5}{3}

STEP 7

implify both sides of the equation.
x=3×53x=3 \times \frac{5}{3}

STEP 8

Multiply the numbers on the right side of the equation.
x=3×53=5x=3 \times \frac{5}{3}=5So, the solution to the equation 13x+3=143\frac{1}{3} x+3=\frac{14}{3} is x=5x=5.

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