Solve 2-{k-[6k-(1-2k)]}=100

$$2 - \{ k - [ 6 k - ( 1 - 2 k ) ] \} = 100$$

Solve for k

$$k = \frac{99}{7} = 14\frac{1}{7} \approx 14.142857143$$

Steps for Solving Linear Equation

To find the opposite of 1-2k, find the opposite of each term.

$$2-\left(k-\left(6k-1-\left(-2k\right)\right)\right)=100$$

The opposite of -2k is 2k.

$$2-\left(k-\left(6k-1+2k\right)\right)=100$$

Combine 6k and 2k to get 8k.

$$2-\left(k-\left(8k-1\right)\right)=100$$

To find the opposite of 8k-1, find the opposite of each term.

$$2-\left(k-8k-\left(-1\right)\right)=100$$

The opposite of -1 is 1.

$$2-\left(k-8k+1\right)=100$$

Combine k and -8k to get -7k.

$$2-\left(-7k+1\right)=100$$

To find the opposite of -7k+1, find the opposite of each term.

$$2-\left(-7k\right)-1=100$$

The opposite of -7k is 7k.

$$2+7k-1=100$$

Subtract 1 from 2 to get 1.

$$1+7k=100$$

Subtract 1 from both sides.

$$7k=100-1$$

Subtract 1 from 100 to get 99.

$$7k=99$$

Divide both sides by 7.

$$k=\frac{99}{7}$$