Solve (sqrt{49}*x-9137.5+100^2-863)-1/14=(154)-4

$$( \sqrt{ 49 } \times x-9137.5+ { 100 }^{ 2 } -863)- \frac{ 1 }{ 14 } =(154)-4$$

Solve for x

$$x = \frac{1054}{49} = 21\frac{25}{49} \approx 21.510204082$$

Steps for Solving Linear Equation

Calculate the square root of 49 and get 7.

$$7x-9137.5+100^{2}-863-\frac{1}{14}=154-4$$

Calculate 100 to the power of 2 and get 10000.

$$7x-9137.5+10000-863-\frac{1}{14}=154-4$$

Add -9137.5 and 10000 to get 862.5.

$$7x+862.5-863-\frac{1}{14}=154-4$$

Subtract 863 from 862.5 to get -0.5.

$$7x-0.5-\frac{1}{14}=154-4$$

Convert decimal number -0.5 to fraction -\frac{5}{10}. Reduce the fraction -\frac{5}{10} to lowest terms by extracting and canceling out 5.

$$7x-\frac{1}{2}-\frac{1}{14}=154-4$$

Least common multiple of 2 and 14 is 14. Convert -\frac{1}{2} and \frac{1}{14} to fractions with denominator 14.

$$7x-\frac{7}{14}-\frac{1}{14}=154-4$$

Since -\frac{7}{14} and \frac{1}{14} have the same denominator, subtract them by subtracting their numerators.

$$7x+\frac{-7-1}{14}=154-4$$

Subtract 1 from -7 to get -8.

$$7x+\frac{-8}{14}=154-4$$

Reduce the fraction \frac{-8}{14} to lowest terms by extracting and canceling out 2.

$$7x-\frac{4}{7}=154-4$$

Subtract 4 from 154 to get 150.

$$7x-\frac{4}{7}=150$$

Add \frac{4}{7} to both sides.

$$7x=150+\frac{4}{7}$$

Convert 150 to fraction \frac{1050}{7}.

$$7x=\frac{1050}{7}+\frac{4}{7}$$

Since \frac{1050}{7} and \frac{4}{7} have the same denominator, add them by adding their numerators.

$$7x=\frac{1050+4}{7}$$

Add 1050 and 4 to get 1054.

$$7x=\frac{1054}{7}$$

Divide both sides by 7.

$$x=\frac{\frac{1054}{7}}{7}$$

Express \frac{\frac{1054}{7}}{7} as a single fraction.

$$x=\frac{1054}{7\times 7}$$

Multiply 7 and 7 to get 49.

$$x=\frac{1054}{49}$$