Question

solve and verify equation 3 /4 (x - 1) = x - 3​

Answer 1

$\huge{\boxed{\boxed{\red{\ulcorner{\mid{\overline{\underline{\bf{Answer:-}}}}}\mid}}}}$

$\huge\red\rightarrow x=\frac{9}{2}\: and\: \frac{-1}{2}$

$\rightarrow \frac{3}{(4)(x - 1)} = x - 3. \\ \\ \rightarrow \: \frac{3}{4x - 4} = x - 3. \\ \\ \rightarrow \: (4x - 4)(x - 3) = 3. \\ \\ \rightarrow \: {4x}^{2} - 12x - 4x + 12 = 3. \\ \\ \rightarrow \: {4x}^{2} - 16x + 9 = 0.$

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Answer 2

Answer:

$x = \frac{9}{2}$

$x = - \frac{1)}{2}$

Step-by-step explanation:

$\frac{3}{4 (x - 1) } = x - 3 \\ \\ \frac{3}{4x - 4} = x - 3 \\ 3 = (x -3 )(4x - 4) \\ 3 = 4x {}^{2} - 4x - 12x + 12 \\ 4x {}^{2} - 4x - 12x + 12 = 3 \\ 4x {}^{2} - 16x + 12 - 3 = 0 \\ 4x {}^{2} - 16x +9 = 0$

now split the equation

$4x {}^{2} - 16x + 9 = 0 \\ 4x {}^{2} - 18x + 2x + 9 \\ 2x(2x - 9) + 1(2x - 9 ) \\ (2x - 9) (2x + 1) \\ x = \frac{9}{2} \: \: \: \: \: or \: \: \: \: \: x = - \frac{1}{2}$