Solve 6-[15x-7(6x-9)-2{10x-5(2-3x)}]

$$6 - [ 15 x - 7 ( 6 x - 9 ) - 2 \{ 10 x - 5 ( 2 - 3 x ) \} ]$$

Evaluate

$$77\left(x-1\right)$$

Solution Steps

Use the distributive property to multiply -7 by 6x-9.

$$6-\left(15x-42x+63-2\left(10x-5\left(2-3x\right)\right)\right)$$

Combine 15x and -42x to get -27x.

$$6-\left(-27x+63-2\left(10x-5\left(2-3x\right)\right)\right)$$

Use the distributive property to multiply -5 by 2-3x.

$$6-\left(-27x+63-2\left(10x-10+15x\right)\right)$$

Combine 10x and 15x to get 25x.

$$6-\left(-27x+63-2\left(25x-10\right)\right)$$

Use the distributive property to multiply -2 by 25x-10.

$$6-\left(-27x+63-50x+20\right)$$

Combine -27x and -50x to get -77x.

$$6-\left(-77x+63+20\right)$$

Add 63 and 20 to get 83.

$$6-\left(-77x+83\right)$$

To find the opposite of -77x+83, find the opposite of each term.

$$6-\left(-77x\right)-83$$

The opposite of -77x is 77x.

$$6+77x-83$$

Subtract 83 from 6 to get -77.

$$-77+77x$$

Expand

$$77x-77$$

Solution Steps

Use the distributive property to multiply -7 by 6x-9.

$$6-\left(15x-42x+63-2\left(10x-5\left(2-3x\right)\right)\right)$$

Combine 15x and -42x to get -27x.

$$6-\left(-27x+63-2\left(10x-5\left(2-3x\right)\right)\right)$$

Use the distributive property to multiply -5 by 2-3x.

$$6-\left(-27x+63-2\left(10x-10+15x\right)\right)$$

Combine 10x and 15x to get 25x.

$$6-\left(-27x+63-2\left(25x-10\right)\right)$$

Use the distributive property to multiply -2 by 25x-10.

$$6-\left(-27x+63-50x+20\right)$$

Combine -27x and -50x to get -77x.

$$6-\left(-77x+63+20\right)$$

Add 63 and 20 to get 83.

$$6-\left(-77x+83\right)$$

To find the opposite of -77x+83, find the opposite of each term.

$$6-\left(-77x\right)-83$$

The opposite of -77x is 77x.

$$6+77x-83$$

Subtract 83 from 6 to get -77.

$$-77+77x$$