Solve (x-1):(1/2+1/3)=4:3

$$( x - 1 ) : ( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) = 4 : 3$$

Solve for x

$$x = \frac{19}{9} = 2\frac{1}{9} \approx 2.111111111$$

Steps for Solving Linear Equation

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

$$\frac{x-1}{\frac{3}{6}+\frac{2}{6}}=\frac{4}{3}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{x-1}{\frac{3+2}{6}}=\frac{4}{3}$$

Add 3 and 2 to get 5.

$$\frac{x-1}{\frac{5}{6}}=\frac{4}{3}$$

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

$$\frac{x}{\frac{5}{6}}+\frac{-1}{\frac{5}{6}}=\frac{4}{3}$$

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

$$\frac{x}{\frac{5}{6}}-\frac{6}{5}=\frac{4}{3}$$

Add \frac{6}{5} to both sides.

$$\frac{x}{\frac{5}{6}}=\frac{4}{3}+\frac{6}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{6}{5} to fractions with denominator 15.

$$\frac{x}{\frac{5}{6}}=\frac{20}{15}+\frac{18}{15}$$

Since \frac{20}{15} and \frac{18}{15} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{5}{6}}=\frac{20+18}{15}$$

Add 20 and 18 to get 38.

$$\frac{x}{\frac{5}{6}}=\frac{38}{15}$$

Multiply both sides by \frac{5}{6}.

$$x=\frac{38}{15}\times \frac{5}{6}$$

Multiply \frac{38}{15} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{38\times 5}{15\times 6}$$

Do the multiplications in the fraction \frac{38\times 5}{15\times 6}.

$$x=\frac{190}{90}$$

Reduce the fraction \frac{190}{90} to lowest terms by extracting and canceling out 10.

$$x=\frac{19}{9}$$