Solve x/3-7(x-2)/9=4-2x-5/6

$$\frac { x } { 3 } - \frac { 7 ( x - 2 ) } { 9 } = 4 - \frac { 2 x - 5 } { 6 }$$

Solve for x

$$x = -\frac{59}{2} = -29\frac{1}{2} = -29.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 3,9,6.

$$6x-2\times 7\left(x-2\right)=72-3\left(2x-5\right)$$

Multiply -2 and 7 to get -14.

$$6x-14\left(x-2\right)=72-3\left(2x-5\right)$$

Use the distributive property to multiply -14 by x-2.

$$6x-14x+28=72-3\left(2x-5\right)$$

Combine 6x and -14x to get -8x.

$$-8x+28=72-3\left(2x-5\right)$$

Use the distributive property to multiply -3 by 2x-5.

$$-8x+28=72-6x+15$$

Add 72 and 15 to get 87.

$$-8x+28=87-6x$$

Add 6x to both sides.

$$-8x+28+6x=87$$

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

$$-2x+28=87$$

Subtract 28 from both sides.

$$-2x=87-28$$

Subtract 28 from 87 to get 59.

$$-2x=59$$

Divide both sides by -2.

$$x=\frac{59}{-2}$$

Fraction \frac{59}{-2} can be rewritten as -\frac{59}{2} by extracting the negative sign.

$$x=-\frac{59}{2}$$