Question about solving for x

[pete-bris]

Hi there I'm in the process of learning algebra and I came across an equation that I'm having some difficulties solving, and it is as follows;

5(x*2)+x = 3(x*2)+x + 2(x-1)+16

My question is; is it possible to multiply a variable and a number inside a parentheses like in the equation above, or are you only allowed to add and subtract?
If it is possible to solve the equation, which I strongly suspect is the case (I just don't know how), could someone please show me how it is done?

Regards

Pete

 

[stapel]

I came across an equation that I'm having some difficulties solving, and it is as follows;

5(x*2)+x = 3(x*2)+x + 2(x-1)+16

My question is; is it possible to multiply a variable and a number inside a parentheses like in the equation above, or are you only allowed to add and subtract?

Yes, one is allowed to multiply inside parentheses. It's odd, and putting the number ("2", in this case) after the variable is extremely odd, but it is mathematically valid. (If you hadn't specified that "x*2" meant "x times two", I'd have guessed that you were using the "*" character to indicate exponentiation, so "x*2" meant "x²", or "x squared".)

Since, as you specify, the 2's are indicating multiplication, then we have:

. . . . .5(x)(2) + x = 3(x)(2) + x + 2(x - 1) + 16

Multiplying out, we get:

. . . . .5*2*x + 1*x = 3*2*x + 1*x + 2(x) + 2(-1) + 16

. . . . .10x + 1x = 6x + 1x + 2x - 2 + 16

. . . . .11x = 9x + 14

Now solve the linear equation in the usual manner.

 

[pete-bris]

Thank you very much, that makes a whole lot more sense!

 

[Otis]

is it possible to multiply a variable and a number inside a parentheses like [this (x*2)]?

x*2 = 2*x

Google Commutative Property of Multiplication :cool: