Question

For the equation 4(2x-4)=8x+k, what value of K will create an equation with infinitely many solutions? Please show steps

Answer 1

Hello!

Getting infinitely many solutions from an equation would be getting a solution that is true but does not include the value of a variable. An example of getting an equation with infinite solutions would be 1=1, or 15.6=15.6.

Let's try to get the same thing on both sides of the equation.

8x-16=8x+k

If we want to get the other side to equal 8x-16, we will need to have k=-16.

8x-16=8x-16

Therefore, our value of k is -16.

I hope this helps!

Answer 2

If you use the distributive property, you will multiply 4 by 2x to get 8x and 4 by -4 to get -16.

8x-16=8x+k

If you want infinitely many solutions the equations on both sides of the equal sign need to be the same. So, k would need to be -16.