If 4x+7 9−3x = 1 4 , then x=[[1]].

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If $\frac{4 x + 7}{9 - 3 x} = \frac{1}{4}$ , then x=[[1]].

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answer is -1.

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Detailed Solution

\frac{4 x + 7}{9 - 3 x} = \frac{1}{4}

, then x= -1.
The given linear equation is as follows,

\frac{4 x + 7}{9 - 3 x} = \frac{1}{4}

.
We first need to eliminate the denominators on both sides of the equation. To do so, we will cross-multiply the denominators with the numerators on the either side as follows and simplify.

4 (4 x + 7) = 1 (9 - 3 x)

\begin{array}{l} 4 (4 x) + 4 (7) = 1 (9) + 1 (- 3 x) \\ 16 x + 28 = 9 - 3 x \end{array}

Subtracting 28 on both sides, we get,

\begin{matrix} 16 x + 28 - 28 = 9 - 3 x - 28 \\ 16 x = - 3 x - 19 \end{matrix}

Adding

3 x

on both sides, we get,

\begin{array}{l} 16 x + 3 x = - 3 x + 3 x - 19 \\ 19 x = - 19 \end{array}

Dividing by 19 on both sides, we get,

x = - 1

So, the value of the variable x is -1.

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