X+7=-2(4x+10)

Question

How do I solve it

Answer 1

Well, that's a douzy! Isn't it?  That would drive most students running to the board, eh? NOT! ;)

X+7=-2(4x+10)

No Sweat! Follow the simple steps and you'll be able to do it again and again.

1. 1X+7=-2(4x+10)

First do distribution. That means, take the number outside the parenthesis, along with its sign, and multiply everything inside the parenthesis by that number. So, it will look like the following once you do that:

x+7=-2(4x)+ -2(10)

1x+7=-8x+(-20) 

2. Next: Get rid of the plus sign next to the -20. Just toss it out! You won't need the plus sign if it's next to a negative number. So, get rid of it.

You now have: 1x+7=-8x-20

3. Next: Combine like terms. Like terms mean that they have identical letters and/or exponents, or just numbers without letters. Ex. 3x + 5x, or 3x^2 + 5x^2, or 3+5. Just add the coefficients (numbers next to those letters) on each side. Ut oh, in this problem, there are no like terms available on the same side. So, skip to step four. Wait, that was too easy. Yay! ;)

4. Now, do the opposites of the signs, to get the numbers and letters together.

1x+7 = -8x-20

 -7           -7

1x= -8x-27

1x+8x=-27

5. Now,combine like terms:

9x=-27

6. Finally, divide by the coefficient (the number next to the variable) on both sides:

9x=-27

9x/9=-27/9

x=-3

Ut Oh, we almost forgot the last step. Don't forget this, or you could end up doing all that work for nothing. Oops! CHECK it out by plugging it in, plugging it in. o--o

(-3)+7=-2(4(-3)+10)

Wherever the x is, I just put in the answer I came up with. Then, I use PEMDAS!

Parenthesis first, exponents next, multiplication or division (whichever comes first) and finally addition or subtraction (whichever comes first...and make sure you go from left to right.)

Let's see...parenthesis first:

(-3) nothing I can do with that, so I'll just take it out of the parenthesis.

-3 + 7 = -2(4(-3)+10)

Next, Let's do the other parenthesis and bring everything else down.

-3 +7 = -2(-12+10)

I can still work some stuff inside that same parenthesis: -3+7 = -2(-2)

Ok, now we have-3+7=-2(-2), so, I'm going to do the next thing in pemdas. No exponents, so I'll do multiplication next. -2(-2) = 4

Now, we do the adding and subtraction, left to right. -3+7=4, and presto: 4=4 so, it appears to work...yippee, yahoo, woohoo! ;)

 

 

 

Answer 2

Always remember the simple rule of P.E.M.D.A.S. Known as the order of operations.

If you use this method start from the left to the right...

Parenthesis | Exponents | Multiplication | Division | Addition | Subtraction

An easy way to remember it is "(P)lease (e)xcuse (m)y (d)ear (a)unt (s)ally."

 

Hope this helps!

-Crystal-

Answer 3

Hi Taylor,

The important thing to do is group the 'x's on one side of the equal sign, and the numbers without 'x's on the other side.  However, before you can do that you need to get the 4x inside the parentheses out of parentheses.

So, first, use the distributive property of multiplication over addition to say:

-2(4x+10) = (-2*4x) + (-2*10)

                = -8x + -20.

Now we can say that x+7=-8x-20.

Now we gather the variable terms (with 'x's) on one side, and the constant terms (without 'x's) on the other side:

                    x + 7 = -8x - 20
                       - 7           -  7                                                                                                                                   x       = -8x  -27                                                                                                                               +8x          +8x                                                                                                                                     9x       =        -27

Now we have 9x, but we want only one x, so we need to divide by 9:

               9x/9 = -27/9

                x = -3.

And just to check my work, I always like to put my answer back into the original equation:

    -3 + 7  = 4  = -2 ((4*-3) + 10) = -2 ( -12 + 10) = -2 * -2 = 4.