Solve 2x+3/5=9x-1/2

$$2 x + \frac { 3 } { 5 } = 9 x - \frac { 1 } { 2 }$$

Solve for x

$$x=\frac{11}{70}\approx 0.157142857$$

Steps for Solving Linear Equation

Subtract 9x from both sides.

$$2x+\frac{3}{5}-9x=-\frac{1}{2}$$

Combine 2x and -9x to get -7x.

$$-7x+\frac{3}{5}=-\frac{1}{2}$$

Subtract \frac{3}{5} from both sides.

$$-7x=-\frac{1}{2}-\frac{3}{5}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{3}{5} to fractions with denominator 10.

$$-7x=-\frac{5}{10}-\frac{6}{10}$$

Since -\frac{5}{10} and \frac{6}{10} have the same denominator, subtract them by subtracting their numerators.

$$-7x=\frac{-5-6}{10}$$

Subtract 6 from -5 to get -11.

$$-7x=-\frac{11}{10}$$

Divide both sides by -7.

$$x=\frac{-\frac{11}{10}}{-7}$$

Express \frac{-\frac{11}{10}}{-7} as a single fraction.

$$x=\frac{-11}{10\left(-7\right)}$$

Multiply 10 and -7 to get -70.

$$x=\frac{-11}{-70}$$

Fraction \frac{-11}{-70} can be simplified to \frac{11}{70} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{11}{70}$$