Solve 1/2x-6=-2/31x-11/32

$$\frac { 1 } { 2 } x - 6 = - \frac { 2 } { 31 } x - \frac { 11 } { 32 }$$

Solve for x

$$x = \frac{5611}{560} = 10\frac{11}{560} \approx 10.019642857$$

Steps for Solving Linear Equation

Add \frac{2}{31}x to both sides.

$$\frac{1}{2}x-6+\frac{2}{31}x=-\frac{11}{32}$$

Combine \frac{1}{2}x and \frac{2}{31}x to get \frac{35}{62}x.

$$\frac{35}{62}x-6=-\frac{11}{32}$$

Add 6 to both sides.

$$\frac{35}{62}x=-\frac{11}{32}+6$$

Convert 6 to fraction \frac{192}{32}.

$$\frac{35}{62}x=-\frac{11}{32}+\frac{192}{32}$$

Since -\frac{11}{32} and \frac{192}{32} have the same denominator, add them by adding their numerators.

$$\frac{35}{62}x=\frac{-11+192}{32}$$

Add -11 and 192 to get 181.

$$\frac{35}{62}x=\frac{181}{32}$$

Multiply both sides by \frac{62}{35}, the reciprocal of \frac{35}{62}.

$$x=\frac{181}{32}\times \frac{62}{35}$$

Multiply \frac{181}{32} times \frac{62}{35} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{181\times 62}{32\times 35}$$

Do the multiplications in the fraction \frac{181\times 62}{32\times 35}.

$$x=\frac{11222}{1120}$$

Reduce the fraction \frac{11222}{1120} to lowest terms by extracting and canceling out 2.

$$x=\frac{5611}{560}$$