Solve 2(x+1)/3(6)-5/9x=2-2x-7/6

$$\frac { 2 ( x + 1 ) } { 3 ( 6 ) } - \frac { 5 } { 9 } x = 2 - \frac { 2 x - 7 } { 6 }$$

Solve for x

$$x = -\frac{55}{2} = -27\frac{1}{2} = -27.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 9,6.

$$2\left(x+1\right)-10x=36-3\left(2x-7\right)$$

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

$$2x+2-10x=36-3\left(2x-7\right)$$

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

$$-8x+2=36-3\left(2x-7\right)$$

Use the distributive property to multiply -3 by 2x-7.

$$-8x+2=36-6x+21$$

Add 36 and 21 to get 57.

$$-8x+2=57-6x$$

Add 6x to both sides.

$$-8x+2+6x=57$$

Combine -8x and 6x to get -2x.

$$-2x+2=57$$

Subtract 2 from both sides.

$$-2x=57-2$$

Subtract 2 from 57 to get 55.

$$-2x=55$$

Divide both sides by -2.

$$x=\frac{55}{-2}$$

Fraction \frac{55}{-2} can be rewritten as -\frac{55}{2} by extracting the negative sign.

$$x=-\frac{55}{2}$$