Solve -2(x-1)+3(4-x)=2(x-3)-5(2x+1)

$$- 2 ( x - 1 ) + 3 ( 4 - x ) = 2 ( x - 3 ) - 5 ( 2 x + 1 )$$

Solve for x

$$x = -\frac{25}{3} = -8\frac{1}{3} \approx -8.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-1.

$$-2x+2+3\left(4-x\right)=2\left(x-3\right)-5\left(2x+1\right)$$

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

$$-2x+2+12-3x=2\left(x-3\right)-5\left(2x+1\right)$$

Add 2 and 12 to get 14.

$$-2x+14-3x=2\left(x-3\right)-5\left(2x+1\right)$$

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

$$-5x+14=2\left(x-3\right)-5\left(2x+1\right)$$

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

$$-5x+14=2x-6-5\left(2x+1\right)$$

Use the distributive property to multiply -5 by 2x+1.

$$-5x+14=2x-6-10x-5$$

Combine 2x and -10x to get -8x.

$$-5x+14=-8x-6-5$$

Subtract 5 from -6 to get -11.

$$-5x+14=-8x-11$$

Add 8x to both sides.

$$-5x+14+8x=-11$$

Combine -5x and 8x to get 3x.

$$3x+14=-11$$

Subtract 14 from both sides.

$$3x=-11-14$$

Subtract 14 from -11 to get -25.

$$3x=-25$$

Divide both sides by 3.

$$x=\frac{-25}{3}$$

Fraction \frac{-25}{3} can be rewritten as -\frac{25}{3} by extracting the negative sign.

$$x=-\frac{25}{3}$$