Solve 2200+x=5/7*(600-1600+x/6)

$$2200+x= \frac{ 5 }{ 7 } \times (600- \frac{ 1600+x }{ 6 } )$$

Solve for x

$$x = -\frac{82400}{47} = -1753\frac{9}{47} \approx -1753.191489362$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 7,6.

$$92400+42x=30\left(600-\frac{1600+x}{6}\right)$$

Use the distributive property to multiply 30 by 600-\frac{1600+x}{6}.

$$92400+42x=18000+30\left(-\frac{1600+x}{6}\right)$$

Cancel out 6, the greatest common factor in 30 and 6.

$$92400+42x=18000-5\left(1600+x\right)$$

Use the distributive property to multiply -5 by 1600+x.

$$92400+42x=18000-8000-5x$$

Subtract 8000 from 18000 to get 10000.

$$92400+42x=10000-5x$$

Add 5x to both sides.

$$92400+42x+5x=10000$$

Combine 42x and 5x to get 47x.

$$92400+47x=10000$$

Subtract 92400 from both sides.

$$47x=10000-92400$$

Subtract 92400 from 10000 to get -82400.

$$47x=-82400$$

Divide both sides by 47.

$$x=\frac{-82400}{47}$$

Fraction \frac{-82400}{47} can be rewritten as -\frac{82400}{47} by extracting the negative sign.

$$x=-\frac{82400}{47}$$