Solve -8(-5x-2)=6x-(-x-7)-2(-x+3)

$$- 8 ( - 5 x - 2 ) = 6 x - ( - x - 7 ) - 2 ( - x + 3 )$$

Solve for x

$$x=-\frac{15}{31}\approx -0.483870968$$

Steps for Solving Linear Equation

Use the distributive property to multiply -8 by -5x-2.

$$40x+16=6x-\left(-x-7\right)-2\left(-x+3\right)$$

To find the opposite of -x-7, find the opposite of each term.

$$40x+16=6x-\left(-x\right)-\left(-7\right)-2\left(-x+3\right)$$

The opposite of -7 is 7.

$$40x+16=6x-\left(-x\right)+7-2\left(-x+3\right)$$

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

$$40x+16=6x-\left(-x\right)+7-2\left(-x\right)-6$$

Multiply -2 and -1 to get 2.

$$40x+16=6x-\left(-x\right)+7+2x-6$$

Combine 6x and 2x to get 8x.

$$40x+16=8x-\left(-x\right)+7-6$$

Subtract 6 from 7 to get 1.

$$40x+16=8x-\left(-x\right)+1$$

Subtract 8x from both sides.

$$40x+16-8x=-\left(-x\right)+1$$

Combine 40x and -8x to get 32x.

$$32x+16=-\left(-x\right)+1$$

Add -x to both sides.

$$32x+16-x=1$$

Subtract 16 from both sides.

$$32x-x=1-16$$

Subtract 16 from 1 to get -15.

$$32x-x=-15$$

Combine 32x and -x to get 31x.

$$31x=-15$$

Divide both sides by 31.

$$x=\frac{-15}{31}$$

Fraction \frac{-15}{31} can be rewritten as -\frac{15}{31} by extracting the negative sign.

$$x=-\frac{15}{31}$$