x squared appearing in the simplification of the equation

[CharlieDoggers]

Hi everyone,

I'm stuck with trying to understand how the values resulted from this equation (see screenshot below). To the best of my current ability, I can understand that 6x in the first bracket on the LHS multiplied by first x value in the second bracket also on the LHS can result in 6x2 (but I'm not even sure about that), but after that everything becomes completely confusing as to how they reached those values.

Any help would be greatly appreciated!

 

[Deleted member 4993]

Hi everyone,

I'm stuck with trying to understand how the values resulted from this equation (see screenshot below). To the best of my current ability, I can understand that 6x in the first bracket on the LHS multiplied by first x value in the second bracket also on the LHS can result in 6x2 (but I'm not even sure about that), but after that everything becomes completely confusing as to how they reached those values.

Any help would be greatly appreciated!





View attachment 25118

(6x +1) * (x + 1) .............................use distributive property of multiplication

= 6x * (x +1) + 1 * (x + 1)

= 6x * x + 6 * x * 1 + 1 * x + 1 * 1

= 6*x² + 6 * x + 1 * x + 1

= 6*x² + 7 * x + 1

If you have any doubt regarding any of the steps................please let us know.

 

[CharlieDoggers]

Thank you so much

 

[JeffM]

Hi everyone,

I'm stuck with trying to understand how the values resulted from this equation (see screenshot below). To the best of my current ability, I can understand that 6x in the first bracket on the LHS multiplied by first x value in the second bracket also on the LHS can result in 6x2 (but I'm not even sure about that), but after that everything becomes completely confusing as to how they reached those values.

Any help would be greatly appreciated!





View attachment 25118

[MATH]\dfrac{6x + 1}{2x - 5} = \dfrac{3x - 2}{x + 1} \implies (2x - 5)(x + 1) * \dfrac{6x + 1}{2x - 5} = (2x - 5)(x + 1) * \dfrac{3x - 2}{x + 1}.[/MATH]
Any trouble there? That’s what was meant by cross-multiplying.

[MATH]\therefore (x + 1)(6x + 1) = (2x - 5)(3x - 2). [/MATH]
Do you see how we get that?

[MATH]\therefore 6x^2 + 7x + 1 = 6x^2 - 19x + 10.[/MATH]
That’s just “expanding the brackets” on both sides. Do you follow that?

[MATH]\therefore - 6x^2 + 6x^2 + 7x + 1 = - 6x^2 + 6x^2 - 19x + 10.[/MATH]
Just subtracting [MATH]6x^2[/MATH] FROM BOTH SIDES OF THE EQUATION.

But that leaves us with the following linear equation.

[MATH]\therefore 7x + 1 = - 19x + 10.[/MATH]
Any questions?

Can you solve that?