Solve x-2/3-2x-3/4=x-1

$$\frac{ x-2 }{ 3 } - \frac{ 2x-3 }{ 4 } =x-1$$

Solve for x

$$x=\frac{13}{14}\approx 0.928571429$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4\left(x-2\right)-3\left(2x-3\right)=12x-12$$

Use the distributive property to multiply 4 by x-2.

$$4x-8-3\left(2x-3\right)=12x-12$$

Use the distributive property to multiply -3 by 2x-3.

$$4x-8-6x+9=12x-12$$

Combine 4x and -6x to get -2x.

$$-2x-8+9=12x-12$$

Add -8 and 9 to get 1.

$$-2x+1=12x-12$$

Subtract 12x from both sides.

$$-2x+1-12x=-12$$

Combine -2x and -12x to get -14x.

$$-14x+1=-12$$

Subtract 1 from both sides.

$$-14x=-12-1$$

Subtract 1 from -12 to get -13.

$$-14x=-13$$

Divide both sides by -14.

$$x=\frac{-13}{-14}$$

Fraction \frac{-13}{-14} can be simplified to \frac{13}{14} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{13}{14}$$