2(x+4)=3(x-2)

 Just a second confirmation

2(x+4)=3(x-2)

distributive property

2x + 8 = 3x - 6

8 = 3x - 2x - 6

8 = x -6

8 + 6 = x

14 = x

1. Open the brackets: 2x+8=3x-6

2. Rearrange the like terms: 8+6=3x-2x

Answer: 14=x; x=14

2(x+4)=3(x-2)
This looks like a call for the distributive property to me. The numbers 2 and 3 adjacent to the parentheses () mean multiplication. The distributive property tells you how to multiply the 2 times the (x+4). Here is how. (* means multiplication)

2*x +2*4= 3*x+3*(-2)

See how the 2 got multiplied by each term inside the parentheses on the left side. And the three got multiplied against each term inside the parentheses on the right side of the equal sign.

Now we just simplify.

2x+8=3x-6

The next step is to move the x terms to one side and the number-only terms to the other. I will choose to move the x's to the right and the number-only terms to the left. I do this by adding or subtracting the same thing from each side.

2x+8-2x=3x-6-2x
I subtracted a 2x from each side. What you do to one side you can do to the other side. Now simplify. 2x-2x cancels out on the left.
8=x-6
Now I add 6 to both sides to move the 6 to left.
8+6=x-6+6
14=x

2(x +4 ) = 3(x-2)         I use the Acronym   D.A.M.N.D.    To help my students remember the order in which they perform these operations

2(x + 4) = 3(x-2)

2*x + 2*4  = 3*x - 3*2          D.  istribute

2x + 8       = 3x - 6                 A. dd like terms (doesn't apply here so next step)

2x  +8       =  3x -6

-3x               -3x                    M. ove the letters 

 -x   + 8    =   -6                    

        -8          -8                    N. ow the numbers

-x     =   -14           (negative because signs are opposite so the larger # determins sign of answer)

-x/-1   =   -14/-1                      D. ivision Last

x   = 14       (neg/neg= pos)

Always check your answer   2(x+4) = 3(x-2)

                                         2(14+4) = 3(14-2)

                                       2(18) = 3(12)

                                       36 = 36    checks

Problem: 2(x+4) = 3(x-2)

Solution:

Step 1: Distribute the 2 to both terms in parenthesis on the left side of the equation.
2 times x = 2x
2 times 4 = 8
So the left side of the equation is now 2x + 8.

Step 2: Distribute the 3 to both terms in parenthesis on the right side of the equation.
3 times x = 3x
3 times 2 = 6
So the right side of the equation is now 3x - 6.

Step 3: Now that we have 2x + 8 = 3x - 6 we can combine like terms.
Subtract 2x from both sides of the equation to get 8 = x - 6.
Add 6 to both sides of the equation to get 14 = x.

Answer: x = 14

When solving a equation (has an equal sign) that has the same variable (x) on both sides of the equation we must get the x's on one side of the equation and the constants (no variables like 8 or -6) on the other side of the equation.  But in this case before we do that we must 1st simplify each side of the equation using the Distributive Property: a(b+c) = ab + ac, or 3(x - 2)= 3x -6.  So,

   2(x + 4) = 3(x - 2)  becomes

       2x + 8 = 3x - 6   now subtract 2x from both sides of the equation (to combine the x's)

2x - 2x + 8 = 3x - 2x -6   which gives us

                8 = x - 6   now add 6 to both sides (combine the constants on the other side from x's)

          8 + 6 = x - 6  + 6   which gives us

               14 = x  or x = 14   now you can check your answer.

      2(x + 4) = 3(x - 2)   substitute 14 for x on both sides

    2(14 + 4) = 3(14 - 2)   simplify the parenthesis

          2(18) = 3(12)   simplify each side

               36 = 36   now we not only solved the problem, but we proved that x = 14 is correct!!