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QuestionSolve the equation: 14(x+12)=78\frac{1}{4}\left(x+\frac{1}{2}\right)=\frac{7}{8}.

Studdy Solution

STEP 1

Assumptions1. The equation is 14(x+1)=78\frac{1}{4}\left(x+\frac{1}{}\right)=\frac{7}{8}

STEP 2

First, we need to distribute the 14\frac{1}{4} to both terms inside the parentheses on the left side of the equation.
14⋅x+14⋅12=78\frac{1}{4} \cdot x + \frac{1}{4} \cdot \frac{1}{2} = \frac{7}{8}

STEP 3

implify the left side of the equation.
1x+18=78\frac{1}{}x + \frac{1}{8} = \frac{7}{8}

STEP 4

Next, we need to isolate the variable xx on one side of the equation. We can do this by subtracting 18\frac{1}{8} from both sides of the equation.
14x+18−18=78−18\frac{1}{4}x + \frac{1}{8} - \frac{1}{8} = \frac{7}{8} - \frac{1}{8}

STEP 5

implify both sides of the equation.
14x=8\frac{1}{4}x = \frac{}{8}

STEP 6

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 by 44.
4⋅14x=4⋅684 \cdot \frac{1}{4}x =4 \cdot \frac{6}{8}

STEP 7

implify both sides of the equation.
x=24x = \frac{24}{}

STEP 8

implify the right side of the equation to find the value of xx.
x=3x =3So, the solution to the equation 14(x+12)=78\frac{1}{4}\left(x+\frac{1}{2}\right)=\frac{7}{8} is x=3x =3.

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