# Simplify as far as possible, sovle the equation, sovle the quadratic equations

• Apr 22nd 2009, 04:05 AM
Steven777
Simplify as far as possible, sovle the equation, sovle the quadratic equations
Simlify as far as possible

(i) 10y-5x+7x-3y-x-2y

(ii) 4(6x-7)-5(2x-3)

Sovle the equation

(i) 8x-9 = 4x-21

(ii) 2(2x-5)=4(2x-1)

(iii) 5-3x
----------- = 5 - x
4

(i) 3x² - x - 2 = 0

(ii) x² - 32 - 4x

I will appreciate if someone can help

thank you
• Apr 22nd 2009, 04:28 AM
stapel
Quote:

Originally Posted by Steven777
Simlify as far as possible

(i) 10y-5x+7x-3y-x-2y

(ii) 4(6x-7)-5(2x-3)

To learn how to add polynomials and combine "like" terms, try here and here. To learn how to work with parentheses, try here.

Quote:

Originally Posted by Steven777
Sovle the equation

(i) 8x-9 = 4x-21

(ii) 2(2x-5)=4(2x-1)

(iii) 5-3x
----------- = 5 - x
4

To learn how to solve linear equations, try here.

Quote:

Originally Posted by Steven777

(i) 3x² - x - 2 = 0

(ii) x² - 32 - 4x

To learn how to solve quadratic equations, try here.

Once you have learned the basic terms and techniques, please attempt at least one exercise from each of the three sets above. If you get stuck, you will then be able to reply with a clear listing of your work and reasoning so far.

Thank you! :D
• Apr 22nd 2009, 11:43 PM
wik_chick88
Quote:

Originally Posted by Steven777
Simplify as far as possible

(i) 10y-5x+7x-3y-x-2y

(ii) 4(6x-7)-5(2x-3)

(i)
$\displaystyle = 10y - 3y - 2y - 5x + 7x - x$
$\displaystyle = 5y + x$

(ii)
$\displaystyle = 4 \times 6x - 4 \times 7 - 5 \times 2x - 5 \times -3$
$\displaystyle = 24x - 28 - 10x +15$
$\displaystyle = 24x - 10x - 28 + 15$
$\displaystyle = 14x - 13$

Quote:

Solve the equation

(i) 8x-9 = 4x-21

(ii) 2(2x-5)=4(2x-1)

(iii) 5-3x
----------- = 5 - x
4
(i)
$\displaystyle 8x - 4x = -21 + 9$
$\displaystyle 4x = -12$
$\displaystyle x = -3$

(ii)
$\displaystyle 2 \times 2x + 2 \times -5 = 4 \times 2x + 4 \times -1$
$\displaystyle 4x -10 = 8x -4$
$\displaystyle -10 + 4 = 8x - 4x$
$\displaystyle -6 = 4x$
$\displaystyle x = -1.5$

(iii) dont understand what you have written for this question

Quote:

(i) 3x² - x - 2 = 0

(ii) x² - 32 - 4x
(i)ok the way i was taught to solve these quadratic equations...

first you write it in the form $\displaystyle ax^2 + bx + c$, thus for this question, $\displaystyle a = 3, b = -1, c = -2$.

Then you work out $\displaystyle ac$, which is $\displaystyle ac = 3 \times -2 = -6$.

Now you have to find two numbers that multiply to give an answer of $\displaystyle -6$ and add to give an answer of $\displaystyle -1$ (which is $\displaystyle b$ in this question).

These two numbers are $\displaystyle -3$ and $\displaystyle 2$ ($\displaystyle -3 \times 2 = -6$ and $\displaystyle -3 + 2 = -1$).

So $\displaystyle 3x^2 - x - 2 = 0$ can be rewritten as:
$\displaystyle 3x^2 - 3x + 2x - 2 = 0$
$\displaystyle 3x(x - 1) + 2(x - 1) = 0$
$\displaystyle (3x + 2) (x - 1) = 0$

This means that either $\displaystyle 3x + 2$ or $\displaystyle x - 1$ have to be equal to 0 (or both)

Therefore,
$\displaystyle 3x + 2 = 0$
$\displaystyle 3x = -2$
$\displaystyle x = -\frac{2}{3}$

OR

$\displaystyle x - 1 = 0$
$\displaystyle x = 1$

(ii) have a go at this one by yourself now that I have shown you how to solve quadratic equations