Solve 10-x/10-30=-5-50/-5-25

$$\frac{ 10-x }{ 10-30 } = \frac{ -5-50 }{ -5-25 }$$

Solve for x

$$x = \frac{140}{3} = 46\frac{2}{3} \approx 46.666666667$$

Steps for Solving Linear Equation

Subtract 30 from 10 to get -20.

$$\frac{10-x}{-20}=\frac{-5-50}{-5-25}$$

Multiply both numerator and denominator by -1.

$$\frac{-10+x}{20}=\frac{-5-50}{-5-25}$$

Subtract 50 from -5 to get -55.

$$\frac{-10+x}{20}=\frac{-55}{-5-25}$$

Subtract 25 from -5 to get -30.

$$\frac{-10+x}{20}=\frac{-55}{-30}$$

Reduce the fraction \frac{-55}{-30} to lowest terms by extracting and canceling out -5.

$$\frac{-10+x}{20}=\frac{11}{6}$$

Divide each term of -10+x by 20 to get -\frac{1}{2}+\frac{1}{20}x.

$$-\frac{1}{2}+\frac{1}{20}x=\frac{11}{6}$$

Add \frac{1}{2} to both sides.

$$\frac{1}{20}x=\frac{11}{6}+\frac{1}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{11}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{1}{20}x=\frac{11}{6}+\frac{3}{6}$$

Since \frac{11}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{20}x=\frac{11+3}{6}$$

Add 11 and 3 to get 14.

$$\frac{1}{20}x=\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{20}x=\frac{7}{3}$$

Multiply both sides by 20, the reciprocal of \frac{1}{20}.

$$x=\frac{7}{3}\times 20$$

Express \frac{7}{3}\times 20 as a single fraction.

$$x=\frac{7\times 20}{3}$$

Multiply 7 and 20 to get 140.

$$x=\frac{140}{3}$$