Solve 14x+1/5-8/12=38x

$$14 x + \frac { 1 } { 5 } - \frac { 8 } { 12 } = 38 x$$

Solve for x

$$x=-\frac{7}{360}\approx -0.019444444$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$14x+\frac{1}{5}-\frac{2}{3}=38x$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$14x+\frac{3}{15}-\frac{10}{15}=38x$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$14x+\frac{3-10}{15}=38x$$

Subtract 10 from 3 to get -7.

$$14x-\frac{7}{15}=38x$$

Subtract 38x from both sides.

$$14x-\frac{7}{15}-38x=0$$

Combine 14x and -38x to get -24x.

$$-24x-\frac{7}{15}=0$$

Add \frac{7}{15} to both sides. Anything plus zero gives itself.

$$-24x=\frac{7}{15}$$

Divide both sides by -24.

$$x=\frac{\frac{7}{15}}{-24}$$

Express \frac{\frac{7}{15}}{-24} as a single fraction.

$$x=\frac{7}{15\left(-24\right)}$$

Multiply 15 and -24 to get -360.

$$x=\frac{7}{-360}$$

Fraction \frac{7}{-360} can be rewritten as -\frac{7}{360} by extracting the negative sign.

$$x=-\frac{7}{360}$$