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

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

Solve for x

$$x = -\frac{16}{5} = -3\frac{1}{5} = -3.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by -2x+4.

$$-10x+20+3x-\left(-x+2\right)=5-\left(3x+1\right)+2\left(-4x-1\right)$$

Combine -10x and 3x to get -7x.

$$-7x+20-\left(-x+2\right)=5-\left(3x+1\right)+2\left(-4x-1\right)$$

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

$$-7x+20-\left(-x\right)-2=5-\left(3x+1\right)+2\left(-4x-1\right)$$

Subtract 2 from 20 to get 18.

$$-7x+18-\left(-x\right)=5-\left(3x+1\right)+2\left(-4x-1\right)$$

To find the opposite of 3x+1, find the opposite of each term.

$$-7x+18-\left(-x\right)=5-3x-1+2\left(-4x-1\right)$$

Subtract 1 from 5 to get 4.

$$-7x+18-\left(-x\right)=4-3x+2\left(-4x-1\right)$$

Use the distributive property to multiply 2 by -4x-1.

$$-7x+18-\left(-x\right)=4-3x-8x-2$$

Combine -3x and -8x to get -11x.

$$-7x+18-\left(-x\right)=4-11x-2$$

Subtract 2 from 4 to get 2.

$$-7x+18-\left(-x\right)=2-11x$$

Add 11x to both sides.

$$-7x+18-\left(-x\right)+11x=2$$

Combine -7x and 11x to get 4x.

$$4x+18-\left(-x\right)=2$$

Subtract 18 from both sides.

$$4x-\left(-x\right)=2-18$$

Subtract 18 from 2 to get -16.

$$4x-\left(-x\right)=-16$$

Multiply -1 and -1 to get 1.

$$4x+x=-16$$

Combine 4x and x to get 5x.

$$5x=-16$$

Divide both sides by 5.

$$x=\frac{-16}{5}$$

Fraction \frac{-16}{5} can be rewritten as -\frac{16}{5} by extracting the negative sign.

$$x=-\frac{16}{5}$$