Robert C. answered • 10/01/12

Dr. Robert can help you with Math and Science

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