Question

If you graph both sides of the equation 2(2x + 3) = 4x + 6, what will the graph look like?

Answer 1

Answer:

The graphs are identical and intersect at infinitely many points.  

Step-by-step explanation:

Given the equation

$2(2x + 3) = 4x + 6$

we have to compare the graph of both sides of equation.

$LHS: 2.(2x + 3)$

By distributive property,

$a.(b+c)=a.b+a.c$

$2.(2x + 3)=2.2x+2.3=4x+6$

$\text{The above expression implies 4x+6}$

which is equals to RHS of given equation i.e

$4x+6=4x+6$

The both sides of equation are identical.

Since both sides of equation are identical therefore intersect at infinitely many points.

Option 3 is correct.

Answer 2

Distribute on the left
4x+6=4x+6

Because the equations are exactly the same, they are coinciding and all point intersect. Therefore, there are infinitely many solutions.

Final answer: C