Question

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

Answer 1

Answer:

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

Step-by-step 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:

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