Solve 2009-{[(588-75*x)*4-2]:5+27}*4-221=1000

$$2009 - \{ [ ( 588 - 75 \cdot x ) \cdot 4 - 2 ] : 5 + 27 \} \cdot 4 - 221 = 1000$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5\left(2009-\left(\frac{\left(588-75x\right)\times 4-2}{5}+27\right)\times 4\right)-1105=5000$$

Use the distributive property to multiply 588-75x by 4.

$$5\left(2009-\left(\frac{2352-300x-2}{5}+27\right)\times 4\right)-1105=5000$$

Subtract 2 from 2352 to get 2350.

$$5\left(2009-\left(\frac{2350-300x}{5}+27\right)\times 4\right)-1105=5000$$

Use the distributive property to multiply \frac{2350-300x}{5}+27 by 4.

$$5\left(2009-\left(4\times \frac{2350-300x}{5}+108\right)\right)-1105=5000$$

Express 4\times \frac{2350-300x}{5} as a single fraction.

$$5\left(2009-\left(\frac{4\left(2350-300x\right)}{5}+108\right)\right)-1105=5000$$

Use the distributive property to multiply 4 by 2350-300x.

$$5\left(2009-\left(\frac{9400-1200x}{5}+108\right)\right)-1105=5000$$

To find the opposite of \frac{9400-1200x}{5}+108, find the opposite of each term.

$$5\left(2009-\frac{9400-1200x}{5}-108\right)-1105=5000$$

Subtract 108 from 2009 to get 1901.

$$5\left(1901-\frac{9400-1200x}{5}\right)-1105=5000$$

Use the distributive property to multiply 5 by 1901-\frac{9400-1200x}{5}.

$$9505-5\times \frac{9400-1200x}{5}-1105=5000$$

Express -5\times \frac{9400-1200x}{5} as a single fraction.

$$9505+\frac{-5\left(9400-1200x\right)}{5}-1105=5000$$

Cancel out 5 and 5.

$$9505-\left(9400-1200x\right)-1105=5000$$

To find the opposite of 9400-1200x, find the opposite of each term.

$$9505-9400-\left(-1200x\right)-1105=5000$$

The opposite of -1200x is 1200x.

$$9505-9400+1200x-1105=5000$$

Subtract 9400 from 9505 to get 105.

$$105+1200x-1105=5000$$

Subtract 1105 from 105 to get -1000.

$$-1000+1200x=5000$$

Add 1000 to both sides.

$$1200x=5000+1000$$

Add 5000 and 1000 to get 6000.

$$1200x=6000$$

Divide both sides by 1200.

$$x=\frac{6000}{1200}$$

Divide 6000 by 1200 to get 5.

$$x=5$$