Solve -2left(x-3right)/7--3left(x+3right)/14=1/7+5/7x-frac{-2left(x-4right)}{14}+frac{1}{7}x

$$\frac{ -2 \left( x-3 \right) }{ 7 } - \frac{ -3 \left( x+3 \right) }{ 14 } = \frac{ 1 }{ 7 } + \frac{ 5 }{ 7 } x- \frac{ -2 \left( x-4 \right) }{ 14 } + \frac{ 1 }{ 7 } x$$

Solve for x

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 14, the least common multiple of 7,14.

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

Multiply 2 and -2 to get -4.

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

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

$$-4x+12+3\left(x+3\right)=2+10x+2\left(x-4\right)+2x$$

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

$$-4x+12+3x+9=2+10x+2\left(x-4\right)+2x$$

Combine -4x and 3x to get -x.

$$-x+12+9=2+10x+2\left(x-4\right)+2x$$

Add 12 and 9 to get 21.

$$-x+21=2+10x+2\left(x-4\right)+2x$$

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

$$-x+21=2+10x+2x-8+2x$$

Combine 10x and 2x to get 12x.

$$-x+21=2+12x-8+2x$$

Subtract 8 from 2 to get -6.

$$-x+21=-6+12x+2x$$

Combine 12x and 2x to get 14x.

$$-x+21=-6+14x$$

Subtract 14x from both sides.

$$-x+21-14x=-6$$

Combine -x and -14x to get -15x.

$$-15x+21=-6$$

Subtract 21 from both sides.

$$-15x=-6-21$$

Subtract 21 from -6 to get -27.

$$-15x=-27$$

Divide both sides by -15.

$$x=\frac{-27}{-15}$$

Reduce the fraction \frac{-27}{-15} to lowest terms by extracting and canceling out -3.

$$x=\frac{9}{5}$$