Solve 9x-1/13-5x-8/4=x+6

$$\frac { 9 x - 1 } { 13 } - \frac { 5 x - 8 } { 4 } = x + 6$$

Solve for x

$$x = -\frac{212}{81} = -2\frac{50}{81} \approx -2.617283951$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 52, the least common multiple of 13,4.

$$4\left(9x-1\right)-13\left(5x-8\right)=52x+312$$

Use the distributive property to multiply 4 by 9x-1.

$$36x-4-13\left(5x-8\right)=52x+312$$

Use the distributive property to multiply -13 by 5x-8.

$$36x-4-65x+104=52x+312$$

Combine 36x and -65x to get -29x.

$$-29x-4+104=52x+312$$

Add -4 and 104 to get 100.

$$-29x+100=52x+312$$

Subtract 52x from both sides.

$$-29x+100-52x=312$$

Combine -29x and -52x to get -81x.

$$-81x+100=312$$

Subtract 100 from both sides.

$$-81x=312-100$$

Subtract 100 from 312 to get 212.

$$-81x=212$$

Divide both sides by -81.

$$x=\frac{212}{-81}$$

Fraction \frac{212}{-81} can be rewritten as -\frac{212}{81} by extracting the negative sign.

$$x=-\frac{212}{81}$$