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QuestionSolve the equation 12(x+23)=54\frac{1}{2}\left(x+\frac{2}{3}\right)=\frac{5}{4}.

Studdy Solution

STEP 1

Assumptions1. The equation is 1(x+3)=54\frac{1}{}\left(x+\frac{}{3}\right)=\frac{5}{4}

STEP 2

First, we need to distribute the 12\frac{1}{2} to both terms in the parentheses.
12x+12⋅2=54\frac{1}{2}x + \frac{1}{2} \cdot \frac{2}{} = \frac{5}{4}

STEP 3

Now, simplify the right side of the equation.
12x+13=5\frac{1}{2}x + \frac{1}{3} = \frac{5}{}

STEP 4

Next, we need to isolate xx on one side of the equation. We can do this by subtracting 13\frac{1}{3} from both sides of the equation.
12x=4−13\frac{1}{2}x = \frac{}{4} - \frac{1}{3}

STEP 5

Now, simplify the right side of the equation.To do this, we need to find a common denominator for 54\frac{5}{4} and 13\frac{1}{3}. The least common denominator is12.
12x=1512−412\frac{1}{2}x = \frac{15}{12} - \frac{4}{12}

STEP 6

implify the right side of the equation.
12x=1112\frac{1}{2}x = \frac{11}{12}

STEP 7

Finally, to solve for xx, we need to divide both sides of the equation by 12\frac{1}{2}, which is the same as multiplying by2.
x=2⋅1112x =2 \cdot \frac{11}{12}

STEP 8

implify the right side of the equation.
x=2212x = \frac{22}{12}

STEP 9

implify the fraction to its lowest terms.
x=116x = \frac{11}{6}So, the solution to the equation 2(x+23)=54\frac{}{2}\left(x+\frac{2}{3}\right)=\frac{5}{4} is x=116x = \frac{11}{6}.

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