equations

[gullpacha]

will i know that when you divide both side of an equasion that dont make different because that is same when you add,divide ,multiply,subtract. but i want to know that according to division rule for example 2x=6 when you divide 2x/2 that is equal one x and 6/2 that is 3 so i want to know when you divide 2 by 2 that gives 1 that mean that 2 goes into 2 one time it dont make it 1 to get x so why we read that as a just x though we have 1 group of 2 besite x can you explain for me logically? if you answer me i will thankfull to you
thank you

 

[Dr.Peterson]

Given the equation [MATH]2x = 6[/MATH], we want to solve by transforming the equation into one with only [MATH]x[/MATH] on one side.

If we divide both sides by 2, [MATH]\frac{2x}{2} = \frac{6}{2}[/MATH], the left-hand side equals [MATH]x[/MATH] and the right-hand side equals [MATH]3[/MATH], so the equation is [MATH]x = 3[/MATH], which gives the solution.

You apparently are asking why [MATH]\frac{2x}{2} = x[/MATH]. What is happening here is that we are multiplying [MATH]x[/MATH] by [MATH]2[/MATH], and then dividing by [MATH]2[/MATH]. The division "undoes" the multiplication, leaving us with what we started with, [MATH]x[/MATH].

Or we could say it this way: [MATH]\frac{2x}{2} = \frac{2\cdot x}{2\cdot 1} = \frac{2}{2}\cdot\frac{x}{1} = 1\cdot x = x[/MATH].

 

[Steven G]

If you went to the store and bought 2 of the same item. You paid a total of $3. You want to know how much one item cost. Let x be the cost of one item. You know that 2*x = $3. How would you figure out what x is, that is the cost of one item?