Solve -1(-7(5-x)-6(2-x))-2(-7(2-x)+4(2-x)=

$$- 1 ( - 7 ( 5 - x ) - 6 ( 2 - x ) ) - 2 ( - 7 ( 2 - x ) + 4 ( 2 - x ) =$$

Evaluate

$$59-19x$$

Solution Steps

Use the distributive property to multiply -7 by 5-x.

$$-\left(-35+7x-6\left(2-x\right)\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Use the distributive property to multiply -6 by 2-x.

$$-\left(-35+7x-12+6x\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Subtract 12 from -35 to get -47.

$$-\left(-47+7x+6x\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Combine 7x and 6x to get 13x.

$$-\left(-47+13x\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

To find the opposite of -47+13x, find the opposite of each term.

$$-\left(-47\right)-13x-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

The opposite of -47 is 47.

$$47-13x-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Use the distributive property to multiply -7 by 2-x.

$$47-13x-2\left(-14+7x+4\left(2-x\right)\right)$$

Use the distributive property to multiply 4 by 2-x.

$$47-13x-2\left(-14+7x+8-4x\right)$$

Add -14 and 8 to get -6.

$$47-13x-2\left(-6+7x-4x\right)$$

Combine 7x and -4x to get 3x.

$$47-13x-2\left(-6+3x\right)$$

Use the distributive property to multiply -2 by -6+3x.

$$47-13x+12-6x$$

Add 47 and 12 to get 59.

$$59-13x-6x$$

Combine -13x and -6x to get -19x.

$$59-19x$$

Expand

$$59-19x$$

Solution Steps

Use the distributive property to multiply -7 by 5-x.

$$-\left(-35+7x-6\left(2-x\right)\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Use the distributive property to multiply -6 by 2-x.

$$-\left(-35+7x-12+6x\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Subtract 12 from -35 to get -47.

$$-\left(-47+7x+6x\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Combine 7x and 6x to get 13x.

$$-\left(-47+13x\right)-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

To find the opposite of -47+13x, find the opposite of each term.

$$-\left(-47\right)-13x-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

The opposite of -47 is 47.

$$47-13x-2\left(-7\left(2-x\right)+4\left(2-x\right)\right)$$

Use the distributive property to multiply -7 by 2-x.

$$47-13x-2\left(-14+7x+4\left(2-x\right)\right)$$

Use the distributive property to multiply 4 by 2-x.

$$47-13x-2\left(-14+7x+8-4x\right)$$

Add -14 and 8 to get -6.

$$47-13x-2\left(-6+7x-4x\right)$$

Combine 7x and -4x to get 3x.

$$47-13x-2\left(-6+3x\right)$$

Use the distributive property to multiply -2 by -6+3x.

$$47-13x+12-6x$$

Add 47 and 12 to get 59.

$$59-13x-6x$$

Combine -13x and -6x to get -19x.

$$59-19x$$