Solve 10x-(7x-(4x-(3x-5)))=10x-(7x-(4x+(3x-5)))

$$10x-(7x-(4x-(3x-5)))=10x-(7x-(4x+(3x-5)))$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

To find the opposite of 3x-5, find the opposite of each term.

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

The opposite of -5 is 5.

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

Combine 4x and -3x to get x.

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

To find the opposite of x+5, find the opposite of each term.

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

Combine 7x and -x to get 6x.

$$10x-\left(6x-5\right)=10x-\left(7x-\left(4x+3x-5\right)\right)$$

To find the opposite of 6x-5, find the opposite of each term.

$$10x-6x-\left(-5\right)=10x-\left(7x-\left(4x+3x-5\right)\right)$$

The opposite of -5 is 5.

$$10x-6x+5=10x-\left(7x-\left(4x+3x-5\right)\right)$$

Combine 10x and -6x to get 4x.

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

Combine 4x and 3x to get 7x.

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

To find the opposite of 7x-5, find the opposite of each term.

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

The opposite of -5 is 5.

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

Combine 7x and -7x to get 0.

$$4x+5=10x-5$$

Subtract 10x from both sides.

$$4x+5-10x=-5$$

Combine 4x and -10x to get -6x.

$$-6x+5=-5$$

Subtract 5 from both sides.

$$-6x=-5-5$$

Subtract 5 from -5 to get -10.

$$-6x=-10$$

Divide both sides by -6.

$$x=\frac{-10}{-6}$$

Reduce the fraction \frac{-10}{-6} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{3}$$