Math

QuestionSolve for xx in the equation: 13x+14=512\frac{1}{3} x+\frac{1}{4}=\frac{5}{12}.

Studdy Solution

STEP 1

Assumptions1. The equation given is 13x+14=512\frac{1}{3} x+\frac{1}{4}=\frac{5}{12}

STEP 2

The first step in solving this equation is to isolate the term with the variable xx. We can do this by subtracting 14\frac{1}{4} from both sides of the equation.
1x+1414=51214\frac{1}{} x+\frac{1}{4}-\frac{1}{4}=\frac{5}{12}-\frac{1}{4}

STEP 3

implify the equation.
13x=5121\frac{1}{3} x=\frac{5}{12}-\frac{1}{}

STEP 4

To subtract fractions, we need to have a common denominator. The least common multiple of12 and4 is12. So, we convert 14\frac{1}{4} to 312\frac{3}{12}.
13x=12312\frac{1}{3} x=\frac{}{12}-\frac{3}{12}

STEP 5

Now, subtract the fractions on the right side of the equation.
13x=212\frac{1}{3} x=\frac{2}{12}

STEP 6

implify the fraction on the right side of the equation.
13x=16\frac{1}{3} x=\frac{1}{6}

STEP 7

To solve for xx, we need to get rid of the fraction on the left side of the equation. We can do this by multiplying both sides of the equation by3.
3×13x=3×163 \times \frac{1}{3} x=3 \times \frac{1}{6}

STEP 8

implify the equation.
x=12x=\frac{1}{2}So, the solution to the equation 13x+14=512\frac{1}{3} x+\frac{1}{4}=\frac{5}{12} is x=12x=\frac{1}{2}.

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