Solve 1-3/2+1-x/frac{4{3}-1/2}=2x-1/frac{5{2}}

$$1 - \frac { 3 } { 2 } + \frac { 1 - x } { \frac { 4 } { 3 } - \frac { 1 } { 2 } } = \frac { 2 x - 1 } { \frac { 5 } { 2 } }$$

Solve for x

$$x=\frac{11}{20}=0.55$$

Steps for Solving Linear Equation

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}-\frac{3}{2}+\frac{1-x}{\frac{4}{3}-\frac{1}{2}}=\frac{2x-1}{\frac{5}{2}}$$

Since \frac{2}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-3}{2}+\frac{1-x}{\frac{4}{3}-\frac{1}{2}}=\frac{2x-1}{\frac{5}{2}}$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{2}+\frac{1-x}{\frac{4}{3}-\frac{1}{2}}=\frac{2x-1}{\frac{5}{2}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$-\frac{1}{2}+\frac{1-x}{\frac{8}{6}-\frac{3}{6}}=\frac{2x-1}{\frac{5}{2}}$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}+\frac{1-x}{\frac{8-3}{6}}=\frac{2x-1}{\frac{5}{2}}$$

Subtract 3 from 8 to get 5.

$$-\frac{1}{2}+\frac{1-x}{\frac{5}{6}}=\frac{2x-1}{\frac{5}{2}}$$

Divide each term of 1-x by \frac{5}{6} to get \frac{1}{\frac{5}{6}}+\frac{-x}{\frac{5}{6}}.

$$-\frac{1}{2}+\frac{1}{\frac{5}{6}}+\frac{-x}{\frac{5}{6}}=\frac{2x-1}{\frac{5}{2}}$$

Divide 1 by \frac{5}{6} by multiplying 1 by the reciprocal of \frac{5}{6}.

$$-\frac{1}{2}+1\times \frac{6}{5}+\frac{-x}{\frac{5}{6}}=\frac{2x-1}{\frac{5}{2}}$$

Multiply 1 and \frac{6}{5} to get \frac{6}{5}.

$$-\frac{1}{2}+\frac{6}{5}+\frac{-x}{\frac{5}{6}}=\frac{2x-1}{\frac{5}{2}}$$

Divide -x by \frac{5}{6} to get -\frac{6}{5}x.

$$-\frac{1}{2}+\frac{6}{5}-\frac{6}{5}x=\frac{2x-1}{\frac{5}{2}}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{6}{5} to fractions with denominator 10.

$$-\frac{5}{10}+\frac{12}{10}-\frac{6}{5}x=\frac{2x-1}{\frac{5}{2}}$$

Since -\frac{5}{10} and \frac{12}{10} have the same denominator, add them by adding their numerators.

$$\frac{-5+12}{10}-\frac{6}{5}x=\frac{2x-1}{\frac{5}{2}}$$

Add -5 and 12 to get 7.

$$\frac{7}{10}-\frac{6}{5}x=\frac{2x-1}{\frac{5}{2}}$$

Divide each term of 2x-1 by \frac{5}{2} to get \frac{2x}{\frac{5}{2}}+\frac{-1}{\frac{5}{2}}.

$$\frac{7}{10}-\frac{6}{5}x=\frac{2x}{\frac{5}{2}}+\frac{-1}{\frac{5}{2}}$$

Divide 2x by \frac{5}{2} to get \frac{4}{5}x.

$$\frac{7}{10}-\frac{6}{5}x=\frac{4}{5}x+\frac{-1}{\frac{5}{2}}$$

Divide -1 by \frac{5}{2} by multiplying -1 by the reciprocal of \frac{5}{2}.

$$\frac{7}{10}-\frac{6}{5}x=\frac{4}{5}x-\frac{2}{5}$$

Subtract \frac{4}{5}x from both sides.

$$\frac{7}{10}-\frac{6}{5}x-\frac{4}{5}x=-\frac{2}{5}$$

Combine -\frac{6}{5}x and -\frac{4}{5}x to get -2x.

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

Subtract \frac{7}{10} from both sides.

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

Least common multiple of 5 and 10 is 10. Convert -\frac{2}{5} and \frac{7}{10} to fractions with denominator 10.

$$-2x=-\frac{4}{10}-\frac{7}{10}$$

Since -\frac{4}{10} and \frac{7}{10} have the same denominator, subtract them by subtracting their numerators.

$$-2x=\frac{-4-7}{10}$$

Subtract 7 from -4 to get -11.

$$-2x=-\frac{11}{10}$$

Divide both sides by -2.

$$x=\frac{-\frac{11}{10}}{-2}$$

Express \frac{-\frac{11}{10}}{-2} as a single fraction.

$$x=\frac{-11}{10\left(-2\right)}$$

Multiply 10 and -2 to get -20.

$$x=\frac{-11}{-20}$$

Fraction \frac{-11}{-20} can be simplified to \frac{11}{20} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{11}{20}$$