3( x + 5) + 4( x – 4) = 13

3(x+5)+4(x-4)=13

Here is what I see looking at this problem: the equal sign makes this an equation. There is one variable, x.

Those two observations lead me to think we can solve for a value of x.

The trick here is to apply the order of operations to expand the terms in parentheses. The parentheses here mean multiplication. Distribute the 3 over the x and the 5:

3*x+3*5+4(x-4)=13 I'm using * for multiplication.

3x+15+4(x-4)=13

Do the same with 4:

3x+15+4*x-4*4=13

3x+15+4x-16=13

Now combine the like terms. Terms that contain x are alike. So are the numerical terms.

7x-1=13

We want to isolate the x, so we use the trick that you can add or subtract anything to the equation as long as you do it to both sides. Add 1 to each side:

7x-1+1=13+1

7x=14

Now the last step. You can divide one side of the equation by almost any number, as long as you do the same thing to the other side. I say almost any number, because the one number you can't divide by is zero.

Divide both sides by 7:

7x/7=14/7

x =2

And that's it.

You can check this by plugging 2 into the original equation for x and seeing if it works:

3(x+5)+4(x-4)=13

3(2+5)+4(2-4)=13

3(7)+4(-2)=13

21-8=13

13=13 CHECK

Hi, Shannan.

The number next to the parentheses means that the number is multiplied by what is inside the parentheses. Since there are 2 terms inside that cannot be combined, we "distribute" the number outside by multiplying it by each of the terms inside.

For the 3(x + 5) we will multiply the  3 times x  and  3 times +5. We get:

3x + 15

We do the same thing for the next set of parentheses:

4(x - 4) is  4 times x  and  4 times -4. So it is:

4x - 16

Putting it together we get:

3x + 15 + 4x - 16 = 13

We now have some like terms we can combine, the 3x and +4x, and the +15 and -16. That gives us:

7x - 1 = 13

To solve this, we add 1 to both sides of the equation:

7x - 1 + 1 = 13 + 1

7x = 14

Then divide each side by 7:

7x / 7 = 14 / 7

x = 2

That is our answer, and we can check it by substituting it back into our original equation:

3(2 + 5) + 4(2 - 4) = 13

3(7) + 4(-2) = 21 + (-8) = 13

It works, so   x = 2   is the answer. 

A word of caution! If the problem had a minus sign in the middle, like:

3(x + 5) - 4(x - 4) = 13

We would distribute a negative 4 in the 2nd set of parentheses, multiplying  -4 times x  and
  -4 times -4  to get  -4x + 16

Hope this helps!

Kathye