Solve x-1/4/x-1=1.0049

$$\frac { x - \frac { 1 } { 4 } } { x - 1 } = 1.0049$$

Solve for x

$$x = \frac{7549}{49} = 154\frac{3}{49} \approx 154.06122449$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$x-\frac{1}{4}=1.0049\left(x-1\right)$$

Use the distributive property to multiply 1.0049 by x-1.

$$x-\frac{1}{4}=1.0049x-1.0049$$

Subtract 1.0049x from both sides.

$$x-\frac{1}{4}-1.0049x=-1.0049$$

Combine x and -1.0049x to get -0.0049x.

$$-0.0049x-\frac{1}{4}=-1.0049$$

Add \frac{1}{4} to both sides.

$$-0.0049x=-1.0049+\frac{1}{4}$$

Add -1.0049 and \frac{1}{4} to get -\frac{7549}{10000}.

$$-0.0049x=-\frac{7549}{10000}$$

Divide both sides by -0.0049.

$$x=\frac{-\frac{7549}{10000}}{-0.0049}$$

Express \frac{-\frac{7549}{10000}}{-0.0049} as a single fraction.

$$x=\frac{-7549}{10000\left(-0.0049\right)}$$

Multiply 10000 and -0.0049 to get -49.

$$x=\frac{-7549}{-49}$$

Fraction \frac{-7549}{-49} can be simplified to \frac{7549}{49} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7549}{49}$$