Solve 1078+249+236/906+310+174+x/2=0.83

$$\frac{ \frac{ 1078+249+236 }{ 906+310+174 } +x }{ 2 } = 0.83$$

Solve for x

$$x=\frac{1861}{3475}\approx 0.535539568$$

Steps for Solving Linear Equation

Multiply both sides by 2.

$$\frac{1078+249+236}{906+310+174}+x=0.83\times 2$$

Add 1078 and 249 to get 1327.

$$\frac{1327+236}{906+310+174}+x=0.83\times 2$$

Add 1327 and 236 to get 1563.

$$\frac{1563}{906+310+174}+x=0.83\times 2$$

Add 906 and 310 to get 1216.

$$\frac{1563}{1216+174}+x=0.83\times 2$$

Add 1216 and 174 to get 1390.

$$\frac{1563}{1390}+x=0.83\times 2$$

Multiply 0.83 and 2 to get 1.66.

$$\frac{1563}{1390}+x=1.66$$

Subtract \frac{1563}{1390} from both sides.

$$x=1.66-\frac{1563}{1390}$$

Convert decimal number 1.66 to fraction \frac{166}{100}. Reduce the fraction \frac{166}{100} to lowest terms by extracting and canceling out 2.

$$x=\frac{83}{50}-\frac{1563}{1390}$$

Least common multiple of 50 and 1390 is 6950. Convert \frac{83}{50} and \frac{1563}{1390} to fractions with denominator 6950.

$$x=\frac{11537}{6950}-\frac{7815}{6950}$$

Since \frac{11537}{6950} and \frac{7815}{6950} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{11537-7815}{6950}$$

Subtract 7815 from 11537 to get 3722.

$$x=\frac{3722}{6950}$$

Reduce the fraction \frac{3722}{6950} to lowest terms by extracting and canceling out 2.

$$x=\frac{1861}{3475}$$