General Mathematics Revision and Practice, Part-2

Part 2, Algebra 1, Page-24

2.1 Directed Numbers

Important Rules:

(1)     To add two directed numbers with the same sign, find the sum of the numbers and give the answer the same sign.

                    e. g.     (a)  + 3 + 5 = + 8  ,   (b)   – 3 – 5 = – 8                 

(2)      To add two directed numbers with different signs, find the difference between the numbers and give the answer the sign of the larger number.

                    e. g .    + 7 + (–3) = + 7 – 3 = + 4

                                + 3 + (–7) = + 3 – 7 = – 4

(3)      To subtract a directed number, change its sign and add.

e. g.    +7 – (+5) = + 7 – 5 = + 2

                               +7 – (-5)  = + 7+ 5  = + 12

                               –7 – (+5) = – 7 – 5  = – 12

                               –7 – (–5) = – 7 + 5 = – 2

(4)      When two directed numbers with the same sign are multiplied together, the answer is positive.

                e. g.    (a)    + 3 × (+5) = + 15       (b)    – 3 × (–5) = + 15                       

(5)      When two directed numbers with different signs are multiplied together, the answer is negative.

                e. g.    (a).   – 3 × (+5) = – 15        (b)   + 3 × (–5) = – 15

(6)      When dividing directed numbers, the rules are the same as in   multiplication.

                e. g.    (a)    – 30 ÷ (–5) = + 6  ,     (b)  + 30 × (–5) = – 6

2.3 Brackets and simplifying:  Page-28

      “A term outside a bracket multiplies each of the terms inside the brackets. This is the distributive law.”

   

    Examples:

(1)     2x (x – 2y + z) = 2x2 – 4xy + 2xz

(2)     7y – 4 (2x – 3) = 7y – 8x + 12

     In general,

     Numbers can be added to numbers

     X’s can be added to x’s

     Y’s can be added to y’s

     X2’s can be added to x2’s

     But they must not be mixed.

     

Examples:

(1)    2x + 3y + 3x2 + 2y–x

= x + 5y + 3x2

(2)    7x + 3x (2x – 3)

=7x + 6x2 – 9x

=6x2 – 2x Ans

Exercise 11, Page -30

Solve the following equations :

Solution 1. 2x - 5 =11

                => 2x =11+5

                => x =

                =>x = 8 Ans

Solution 7. -7 = 2x -10

                => 2x - 10= -7

                => 2x = -7+10

               => 2x = 3

                => x = Ans

Solution 10. 5+6x  =7

                => 6x =7 - 5

                => 6x = 2

                => x =

                => x = Ans

Solution 34. 5x - 4 =3 - x

                => 5x+x =3+4

                => 6x = 7

                => x =

                =>x = Ans