Solve 2x-5/6-8x+7/5=6

$$\frac { 2 x - 5 } { 6 } - \frac { 8 x + 7 } { 5 } = 6$$

Solve for x

$$x = -\frac{13}{2} = -6\frac{1}{2} = -6.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 6,5.

$$5\left(2x-5\right)-6\left(8x+7\right)=180$$

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

$$10x-25-6\left(8x+7\right)=180$$

Use the distributive property to multiply -6 by 8x+7.

$$10x-25-48x-42=180$$

Combine 10x and -48x to get -38x.

$$-38x-25-42=180$$

Subtract 42 from -25 to get -67.

$$-38x-67=180$$

Add 67 to both sides.

$$-38x=180+67$$

Add 180 and 67 to get 247.

$$-38x=247$$

Divide both sides by -38.

$$x=\frac{247}{-38}$$

Reduce the fraction \frac{247}{-38} to lowest terms by extracting and canceling out 19.

$$x=-\frac{13}{2}$$