Solve -1/7x-1/2=-1/5

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

Solve for x

$$x = -\frac{21}{10} = -2\frac{1}{10} = -2.1$$

Steps for Solving Linear Equation

Add \frac{1}{2} to both sides.

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

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

$$-\frac{1}{7}x=-\frac{2}{10}+\frac{5}{10}$$

Since -\frac{2}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$-\frac{1}{7}x=\frac{-2+5}{10}$$

Add -2 and 5 to get 3.

$$-\frac{1}{7}x=\frac{3}{10}$$

Multiply both sides by -7, the reciprocal of -\frac{1}{7}.

$$x=\frac{3}{10}\left(-7\right)$$

Express \frac{3}{10}\left(-7\right) as a single fraction.

$$x=\frac{3\left(-7\right)}{10}$$

Multiply 3 and -7 to get -21.

$$x=\frac{-21}{10}$$

Fraction \frac{-21}{10} can be rewritten as -\frac{21}{10} by extracting the negative sign.

$$x=-\frac{21}{10}$$