
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