Question

For what value of x must ABCD be a parallelogram?
?
(15x+5)
(20x-5)

Answer 1

x = 2

Explanation:

A parallelogram is a figure with four sides in total, and two parallel opposite sides.

This means that the opposite sides are equal in length.

For the parallelogram ABCD in this problem, we are told that the length of two opposite sides are:

`15x+5`

and

`20x-5`

The two sides must be equal in order for ABCD to be a parallelogram, so we can write:

`15x+5=20x-5`

And now we solve for x: first, we add +5 on both sides,

`15x+5+5=20x-5+5\\15x+10=20x`

Then we subtract 15x on both sides:

`15x+10-15x=20x-15x\\10=5x`

Finally, we divide both sides by 5:

`x=(10)/(5)=2`