Question

2(x + 3) + 2x = 3x + 12

Answer 1

We can proceed as follows to solve this equation:

$2(x+3)+2x=3x+12$

1. Apply the distributive property on the left side of the equation:

$2\cdot x+2\cdot3+2x=3x+12$

Then, we have:

$2x+6+2x=3x+12$

2. Add the like terms on the left side of the equation:

$2x+2x+6=3x+12\Rightarrow4x+6=3x+12$

3. Subtract 3x to both sides of the equation:

$4x-3x+6=3x-3x+12\Rightarrow x+6=12$

4. Subtract 6 from both sides of the equation:

$x+6-6=12-6\Rightarrow x=6$

Therefore, the value for x in the equation is equal to 6 (x = 6).

We can check this using the original equation:

$2\cdot(x+3)+2x=3x+12\Rightarrow2\cdot(6+3)+2\cdot(6)=3\cdot(6)+12$

Then, we have:

$2\cdot(9)+12=18+12\Rightarrow18+12=18+12\Rightarrow30=30$

As we can see, this is always TRUE. Therefore, the solution x = 6 is correct.