Question

Solve the equation. | 3k-2 | = 2| k+2 |

Answer 1

`-2/5 \text{ and } 6`

Explanation:

So we have the equation:

`|3k-2|=2|k+2|`

First, distribute the 2 into the absolute value:

`|3k-2|=|2k+4|`

Definition of absolute value:

`3k-2=(2k+4) \text{ or } 3k-2=-(2k+4)`

Left:

`3k-2=2k+4`

Subtract 2k from both sides:

`k-2=4`

Add 2 to both sides:

`k=6`

Right:

`3k-2=-(2k+4)`

Distribute the negative:

`3k-2=-2k-4`

Add 2k to both sides:

`5k-2=-4`

Add 2:

`5k=-2`

Divide by 5:

`k=-2/5`

So, our solutions are:

`-2/5 \text{ and } 6`