Date: Wed, 07 Apr 1999 18:56:32 -0700
Sender: Ron
Subject: grade 10 math

the type of question i'm having trouble with is 5(2x-1)=3(x-4)

Hi Ron

I am assuming that the instructions are to solve for x. That is find the value of x that makes the equation 5(2x-1) = 3(x-4) a true statement. The procedure is to start with the equation

5(2x-1) = 3(x-4),

write a sequence of equivalent algebraic sentences and end with a sentance of the form
x = a number.

The first step here is to expand both sides of the equation. The right side is 3(x-4) which is equivalent to 3x -3(4) or 3x - 12. Similarly the left side is 5(2x-1) which is equivalent to 5(2x) - 5(1) or 10x - 5. Thus I have
5(2x-1) = 3(x-4)

and thus
10x - 5 = 3x - 12
Since the goal equation has only an x on the left of the equal sign the next step is to remove the -5 from this side. This you can do by adding 5 to each side of the equation since this rertains the equality. Thus the next step is
hence
10x - 5 + 5= 3x - 12+ 5

or
10x = 3x - 7

Again, since the goal equation has no x on the left side remove the 3x by subtracting 3x from both sides.
Thus
10x - 3x= 3x - 7- 3x
or
7x = - 7

If you now divide both sides by 7 you get
 
x = -1

So here is my solution
 
5(2x-1) = 3(x-4)

and thus
10x - 5 = 3x - 12

hence
10x - 5 + 5= 3x - 12+ 5

or
10x = 3x - 7

Thus
10x - 3x= 3x - 7- 3x

or
7x = - 7

and therefore
x = -1

You can now check that the solution is correct by substituting x = -1 into the original equation to see if the two sides are equal.

Cheers
Penny

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