Summary ALGEBRA - Solve for x

ALGEBRA
>
Usually Question i of Mathematics Paper .
-




1




>
-


Skills show up in
every maths section


Ayanda Nzimande
① BASIC FACTORISING


Examples :




x2
·
-
3x -

10 = 0 ·
Given an equation in standard form


(x 5)(x + 2)
-
= 0 ·
Find factors of last term that produce middle term

x -

5 = 0 or 3 + 2 = 0 ·
Zero factor law


x =
5 C= -


2 · Solve for x-values
, m




·
(xc + 3)(2- 5x) = 0 .
Given already factorised

x+ 3 = 0 or 2-5x = 0 · Zero factor law

x = -
3 -

5x = -

2
p

x =
E ·
solve for x-values




·
4x2 -
17x = 0

JC ( 40c -
(7) = 0 ·
Take out common factor


x =
Op Or 4x-17 = 0 ·
zero factor law

4x = 17

xC =
* p
·
solve for ec-values




② QUADRATIC FORMULA a formula instead of factorising to solve for e-values




Standard form : ax + bx + C
,




C= - b

さ」 ( b )~ - 4 (a) (c)

2 ( a)



*
always correct -values to two decimal places
* use formula when you cannot factorise your quadratic equation

, Examples :




2
。
30℃ + 6x= - 1



3 x2 60 xt 1
t
=
0 ·
Put equation in standard form ( =
0)

x = -
b ±√ ( b) ー
4 ( a) (c) ·
Formula


2 (a)
x =
-

(6) = V(6)2 -

4(3)(1) ·
Sub into formula then use calculator to find -values


2 ( 3)

When +: When-i

3C = - 0, 18 x =
-1 , 82 ·
Correct answers to 2 decimal places
& ,




∞
20cc t 70c -
1 =
0




x = -
b± )b '
-
4 ac

2a

x = -

[7) ± ) (7) -

4 (2) ( ~
)
2 ( 2)


When +: When- :



x = 0 ,
14 C= -
3 , 640
m




③ EXPONENTS equations
·




K-method

>
-
Revise exponent laws




Examples
CALCULATOR :
2x
+4
·
2x + =

8784x Wrote 8704 In its prime factor >
-
'8104'-SHIFT-FACT -2" .
17



℃= 2917
。 +
2 24 2 ·
exponent law - > am + " = aman

2 (24 + 1) =
29 .
17 ·
Common factor of 12
℃
2 ( 17 ) = 2917
29
℃
2 =
·
Divide both sides by 17


CC =
9p .

Drop SAME bases and solve for cc. -am
.
= an
0 m = m