Solve 1-(2x-1)-3(x-2)-4(x-3)={0}_{}

$$1-(2x-1)-3(x-2)-4(x-3)= { 0 }_{ }$$

Solve for x

$$x = \frac{20}{9} = 2\frac{2}{9} \approx 2.222222222$$

Steps for Solving Linear Equation

To find the opposite of 2x-1, find the opposite of each term.

$$1-2x-\left(-1\right)-3\left(x-2\right)-4\left(x-3\right)=0$$

The opposite of -1 is 1.

$$1-2x+1-3\left(x-2\right)-4\left(x-3\right)=0$$

Add 1 and 1 to get 2.

$$2-2x-3\left(x-2\right)-4\left(x-3\right)=0$$

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

$$2-2x-3x+6-4\left(x-3\right)=0$$

Combine -2x and -3x to get -5x.

$$2-5x+6-4\left(x-3\right)=0$$

Add 2 and 6 to get 8.

$$8-5x-4\left(x-3\right)=0$$

Use the distributive property to multiply -4 by x-3.

$$8-5x-4x+12=0$$

Combine -5x and -4x to get -9x.

$$8-9x+12=0$$

Add 8 and 12 to get 20.

$$20-9x=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-9x=-20$$

Divide both sides by -9.

$$x=\frac{-20}{-9}$$

Fraction \frac{-20}{-9} can be simplified to \frac{20}{9} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{20}{9}$$