Solve 90x+1/15x+4000=(78+1/20)x+6600

$$90x+ \frac{ 1 }{ 15 } x+4000=(78+ \frac{ 1 }{ 20 } )x+6600$$

Solve for x

$$x = \frac{156000}{721} = 216\frac{264}{721} \approx 216.366158114$$

Steps for Solving Linear Equation

Combine 90x and \frac{1}{15}x to get \frac{1351}{15}x.

$$\frac{1351}{15}x+4000=\left(78+\frac{1}{20}\right)x+6600$$

Convert 78 to fraction \frac{1560}{20}.

$$\frac{1351}{15}x+4000=\left(\frac{1560}{20}+\frac{1}{20}\right)x+6600$$

Since \frac{1560}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{1351}{15}x+4000=\frac{1560+1}{20}x+6600$$

Add 1560 and 1 to get 1561.

$$\frac{1351}{15}x+4000=\frac{1561}{20}x+6600$$

Subtract \frac{1561}{20}x from both sides.

$$\frac{1351}{15}x+4000-\frac{1561}{20}x=6600$$

Combine \frac{1351}{15}x and -\frac{1561}{20}x to get \frac{721}{60}x.

$$\frac{721}{60}x+4000=6600$$

Subtract 4000 from both sides.

$$\frac{721}{60}x=6600-4000$$

Subtract 4000 from 6600 to get 2600.

$$\frac{721}{60}x=2600$$

Multiply both sides by \frac{60}{721}, the reciprocal of \frac{721}{60}.

$$x=2600\times \frac{60}{721}$$

Express 2600\times \frac{60}{721} as a single fraction.

$$x=\frac{2600\times 60}{721}$$

Multiply 2600 and 60 to get 156000.

$$x=\frac{156000}{721}$$