Solve 3x+5/2-4x-5/3=7x+1/6-5

$$\frac { 3 x + 5 } { 2 } - \frac { 4 x - 5 } { 3 } = \frac { 7 x + 1 } { 6 } - 5$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$3\left(3x+5\right)-2\left(4x-5\right)=7x+1-30$$

Use the distributive property to multiply 3 by 3x+5.

$$9x+15-2\left(4x-5\right)=7x+1-30$$

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

$$9x+15-8x+10=7x+1-30$$

Combine 9x and -8x to get x.

$$x+15+10=7x+1-30$$

Add 15 and 10 to get 25.

$$x+25=7x+1-30$$

Subtract 30 from 1 to get -29.

$$x+25=7x-29$$

Subtract 7x from both sides.

$$x+25-7x=-29$$

Combine x and -7x to get -6x.

$$-6x+25=-29$$

Subtract 25 from both sides.

$$-6x=-29-25$$

Subtract 25 from -29 to get -54.

$$-6x=-54$$

Divide both sides by -6.

$$x=\frac{-54}{-6}$$

Divide -54 by -6 to get 9.

$$x=9$$