Question

determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. afterwards, determine two values of x that support your conclusion. 4(x+4) = 4x+16the equation has ____ solutions.a value of x that makes the equation true is __,which when simplified makes the equation turn into____=_____.a value of x that makes the equation false is____, which when simplified makes the equation turn into ___=___.

Answer 1

4(x+4) = 4x+16

Apply distributive property:

4(x)+4(4)= 4x+16

4x+16=4x+16

Add and subtract alike terms

4x-4x= 16-16

0=0

Since x can have many values, it has an infinite number of solutions.

we can replace x by 1, by 3, by 2 and the equality will remain.

the equation has an infinite number of solutions.