Solve x+60>1000(x/7000+60/1000)

$$x+60 > 1000( \frac{ x }{ 7000 } + \frac{ 60 }{ 1000 } )$$

Solve for x

$$x>0$$

Short Solution Steps

Multiply both sides of the equation by 7000, the least common multiple of 7000,1000. Since 7000 is positive, the inequality direction remains the same.

$$7000x+420000>7000000\left(\frac{x}{7000}+\frac{60}{1000}\right)$$

Reduce the fraction \frac{60}{1000} to lowest terms by extracting and canceling out 20.

$$7000x+420000>7000000\left(\frac{x}{7000}+\frac{3}{50}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7000 and 50 is 7000. Multiply \frac{3}{50} times \frac{140}{140}.

$$7000x+420000>7000000\left(\frac{x}{7000}+\frac{3\times 140}{7000}\right)$$

Since \frac{x}{7000} and \frac{3\times 140}{7000} have the same denominator, add them by adding their numerators.

$$7000x+420000>7000000\times \frac{x+3\times 140}{7000}$$

Do the multiplications in x+3\times 140.

$$7000x+420000>7000000\times \frac{x+420}{7000}$$

Cancel out 7000, the greatest common factor in 7000000 and 7000.

$$7000x+420000>1000\left(x+420\right)$$

Use the distributive property to multiply 1000 by x+420.

$$7000x+420000>1000x+420000$$

Subtract 1000x from both sides.

$$7000x+420000-1000x>420000$$

Combine 7000x and -1000x to get 6000x.

$$6000x+420000>420000$$

Subtract 420000 from both sides.

$$6000x>420000-420000$$

Subtract 420000 from 420000 to get 0.

$$6000x>0$$

Product of two numbers is >0 if both are >0 or both are <0. Since 6000>0, x must be >0.

$$x>0$$