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

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

Solve for x

$$x = -\frac{153}{10} = -15\frac{3}{10} = -15.3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,5,2.

$$10\left(6+7x\right)-6\left(5x-3\right)=30x-75$$

Use the distributive property to multiply 10 by 6+7x.

$$60+70x-6\left(5x-3\right)=30x-75$$

Use the distributive property to multiply -6 by 5x-3.

$$60+70x-30x+18=30x-75$$

Combine 70x and -30x to get 40x.

$$60+40x+18=30x-75$$

Add 60 and 18 to get 78.

$$78+40x=30x-75$$

Subtract 30x from both sides.

$$78+40x-30x=-75$$

Combine 40x and -30x to get 10x.

$$78+10x=-75$$

Subtract 78 from both sides.

$$10x=-75-78$$

Subtract 78 from -75 to get -153.

$$10x=-153$$

Divide both sides by 10.

$$x=\frac{-153}{10}$$

Fraction \frac{-153}{10} can be rewritten as -\frac{153}{10} by extracting the negative sign.

$$x=-\frac{153}{10}$$