Solve 7x+14/3-17-3x/5=6x-4x+2/3-5

$$\frac{ 7x+14 }{ 3 } - \frac{ 17-3x }{ 5 } =6x- \frac{ 4x+2 }{ 3 } -5$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(7x+14\right)-3\left(17-3x\right)=90x-5\left(4x+2\right)-75$$

Use the distributive property to multiply 5 by 7x+14.

$$35x+70-3\left(17-3x\right)=90x-5\left(4x+2\right)-75$$

Use the distributive property to multiply -3 by 17-3x.

$$35x+70-51+9x=90x-5\left(4x+2\right)-75$$

Subtract 51 from 70 to get 19.

$$35x+19+9x=90x-5\left(4x+2\right)-75$$

Combine 35x and 9x to get 44x.

$$44x+19=90x-5\left(4x+2\right)-75$$

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

$$44x+19=90x-20x-10-75$$

Combine 90x and -20x to get 70x.

$$44x+19=70x-10-75$$

Subtract 75 from -10 to get -85.

$$44x+19=70x-85$$

Subtract 70x from both sides.

$$44x+19-70x=-85$$

Combine 44x and -70x to get -26x.

$$-26x+19=-85$$

Subtract 19 from both sides.

$$-26x=-85-19$$

Subtract 19 from -85 to get -104.

$$-26x=-104$$

Divide both sides by -26.

$$x=\frac{-104}{-26}$$

Divide -104 by -26 to get 4.

$$x=4$$