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QuestionFind the value of 13x−34\frac{1}{3}x - \frac{3}{4} for x=14x=\frac{1}{4}.

Studdy Solution

STEP 1

Assumptions1. The variable xx in the expression 13x−34\frac{1}{3}x - \frac{3}{4} is given as x=14x=\frac{1}{4}

STEP 2

We need to substitute the value of xx into the expression.1x−4=1(14)−4\frac{1}{}x - \frac{}{4} = \frac{1}{}(\frac{1}{4}) - \frac{}{4}

STEP 3

Now, we need to calculate the value of the expression after substituting xx.
13(1)−3=112−3\frac{1}{3}(\frac{1}{}) - \frac{3}{} = \frac{1}{12} - \frac{3}{}

STEP 4

To subtract these fractions, we need to find a common denominator. The least common multiple of12 and4 is12. So, we convert 34\frac{3}{4} to a fraction with12 as the denominator.
34=3×34×3=912\frac{3}{4} = \frac{3 \times3}{4 \times3} = \frac{9}{12}

STEP 5

Substitute 912\frac{9}{12} back into the expression and do the subtraction.
112−912=−812\frac{1}{12} - \frac{9}{12} = -\frac{8}{12}

STEP 6

implify the fraction −812-\frac{8}{12} by dividing the numerator and the denominator by their greatest common divisor, which is4.
−812=−8÷412÷4=−23-\frac{8}{12} = -\frac{8 \div4}{12 \div4} = -\frac{2}{3}So, the value of the expression 13x−34\frac{1}{3}x - \frac{3}{4} when x=14x=\frac{1}{4} is −23-\frac{2}{3}.

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