Solve 4x-{12-[17-(5-x)2+x]-x}=3x-[7x-(2x+10)]-3

$$4 x - \{ 12 - [ 17 - ( 5 - x ) 2 + x ] - x \} = 3 x - [ 7 x - ( 2 x + 10 ) ] - 3$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5-x by 2.

$$4x-\left(12-\left(17-\left(10-2x\right)+x\right)-x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

To find the opposite of 10-2x, find the opposite of each term.

$$4x-\left(12-\left(17-10-\left(-2x\right)+x\right)-x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

The opposite of -2x is 2x.

$$4x-\left(12-\left(17-10+2x+x\right)-x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

Subtract 10 from 17 to get 7.

$$4x-\left(12-\left(7+2x+x\right)-x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

Combine 2x and x to get 3x.

$$4x-\left(12-\left(7+3x\right)-x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

To find the opposite of 7+3x, find the opposite of each term.

$$4x-\left(12-7-3x-x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

Subtract 7 from 12 to get 5.

$$4x-\left(5-3x-x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

Combine -3x and -x to get -4x.

$$4x-\left(5-4x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

To find the opposite of 5-4x, find the opposite of each term.

$$4x-5-\left(-4x\right)=3x-\left(7x-\left(2x+10\right)\right)-3$$

The opposite of -4x is 4x.

$$4x-5+4x=3x-\left(7x-\left(2x+10\right)\right)-3$$

Combine 4x and 4x to get 8x.

$$8x-5=3x-\left(7x-\left(2x+10\right)\right)-3$$

To find the opposite of 2x+10, find the opposite of each term.

$$8x-5=3x-\left(7x-2x-10\right)-3$$

Combine 7x and -2x to get 5x.

$$8x-5=3x-\left(5x-10\right)-3$$

To find the opposite of 5x-10, find the opposite of each term.

$$8x-5=3x-5x-\left(-10\right)-3$$

The opposite of -10 is 10.

$$8x-5=3x-5x+10-3$$

Combine 3x and -5x to get -2x.

$$8x-5=-2x+10-3$$

Subtract 3 from 10 to get 7.

$$8x-5=-2x+7$$

Add 2x to both sides.

$$8x-5+2x=7$$

Combine 8x and 2x to get 10x.

$$10x-5=7$$

Add 5 to both sides.

$$10x=7+5$$

Add 7 and 5 to get 12.

$$10x=12$$

Divide both sides by 10.

$$x=\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{6}{5}$$