Solve 4+varepsilon_{1}-[2-(-5-1)+(-3+2)]-[-2+(2-5)-(-3+3)]=

$$4 + \varepsilon _ { 1 } - [ 2 - ( - 5 - 1 ) + ( - 3 + 2 ) ] - [ - 2 + ( 2 - 5 ) - ( - 3 + 3 ) ] =$$

Evaluate

$$\epsilon _{1}+2$$

Solution Steps

Subtract 1 from -5 to get -6.

$$4+\epsilon _{1}-\left(2-\left(-6\right)-3+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

The opposite of -6 is 6.

$$4+\epsilon _{1}-\left(2+6-3+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

Add 2 and 6 to get 8.

$$4+\epsilon _{1}-\left(8-3+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

Subtract 3 from 8 to get 5.

$$4+\epsilon _{1}-\left(5+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

Add 5 and 2 to get 7.

$$4+\epsilon _{1}-7-\left(-2+2-5-\left(-3+3\right)\right)$$

Subtract 7 from 4 to get -3.

$$-3+\epsilon _{1}-\left(-2+2-5-\left(-3+3\right)\right)$$

Add -2 and 2 to get 0.

$$-3+\epsilon _{1}-\left(-5-\left(-3+3\right)\right)$$

Add -3 and 3 to get 0.

$$-3+\epsilon _{1}-\left(-5-0\right)$$

Subtract 0 from -5 to get -5.

$$-3+\epsilon _{1}-\left(-5\right)$$

The opposite of -5 is 5.

$$-3+\epsilon _{1}+5$$

Add -3 and 5 to get 2.

$$2+\epsilon _{1}$$

Expand

$$\epsilon _{1}+2$$

Solution Steps

Subtract 1 from -5 to get -6.

$$4+\epsilon _{1}-\left(2-\left(-6\right)-3+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

The opposite of -6 is 6.

$$4+\epsilon _{1}-\left(2+6-3+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

Add 2 and 6 to get 8.

$$4+\epsilon _{1}-\left(8-3+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

Subtract 3 from 8 to get 5.

$$4+\epsilon _{1}-\left(5+2\right)-\left(-2+2-5-\left(-3+3\right)\right)$$

Add 5 and 2 to get 7.

$$4+\epsilon _{1}-7-\left(-2+2-5-\left(-3+3\right)\right)$$

Subtract 7 from 4 to get -3.

$$-3+\epsilon _{1}-\left(-2+2-5-\left(-3+3\right)\right)$$

Add -2 and 2 to get 0.

$$-3+\epsilon _{1}-\left(-5-\left(-3+3\right)\right)$$

Add -3 and 3 to get 0.

$$-3+\epsilon _{1}-\left(-5-0\right)$$

Subtract 0 from -5 to get -5.

$$-3+\epsilon _{1}-\left(-5\right)$$

The opposite of -5 is 5.

$$-3+\epsilon _{1}+5$$

Add -3 and 5 to get 2.

$$2+\epsilon _{1}$$