Solve -11x+14-1=1/5+1/2

$$- 11 x + 14 - 1 = \frac { 1 } { 5 } + \frac { 1 } { 2 }$$

Solve for x

$$x = \frac{123}{110} = 1\frac{13}{110} \approx 1.118181818$$

Steps for Solving Linear Equation

Subtract 1 from 14 to get 13.

$$-11x+13=\frac{1}{5}+\frac{1}{2}$$

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

$$-11x+13=\frac{2}{10}+\frac{5}{10}$$

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

$$-11x+13=\frac{2+5}{10}$$

Add 2 and 5 to get 7.

$$-11x+13=\frac{7}{10}$$

Subtract 13 from both sides.

$$-11x=\frac{7}{10}-13$$

Convert 13 to fraction \frac{130}{10}.

$$-11x=\frac{7}{10}-\frac{130}{10}$$

Since \frac{7}{10} and \frac{130}{10} have the same denominator, subtract them by subtracting their numerators.

$$-11x=\frac{7-130}{10}$$

Subtract 130 from 7 to get -123.

$$-11x=-\frac{123}{10}$$

Divide both sides by -11.

$$x=\frac{-\frac{123}{10}}{-11}$$

Express \frac{-\frac{123}{10}}{-11} as a single fraction.

$$x=\frac{-123}{10\left(-11\right)}$$

Multiply 10 and -11 to get -110.

$$x=\frac{-123}{-110}$$

Fraction \frac{-123}{-110} can be simplified to \frac{123}{110} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{123}{110}$$