Basic Algebra and Algebraic Manipulation

Question 1

given what x=5 and y=-3, evaluate
(a) 3x - 2y
(b) 2y/3x

Answer 1

(a) 21
(b) - 2/5

Question 2

linear expression definition

Answer 2

A linear expression in one variable x is an algebraic expression that contains only one term in x, with or without a constant term.

Question 3

is 4x + y - 8 a linear expression

Answer 3

yes. it is a linear expression in two variables x and y

Question 4

like terms definition

Answer 4

Like terms contain the same variable(s) raised to the same power.

Question 5

unlike terms

Answer 5

Unlike terms contain the different variable(s) raised to the same power.

Question 6

4x + (-7x)

Answer 6

-3x

Question 7

-9x + 8x

Answer 7

-x

Question 8

-3y - 4y

Answer 8

-7y

Question 9

-6y - (-2y)

Answer 9

-4y

Question 10

-5x + (-6y) - 3x -(-4y)

Answer 10

-8x - 2y

Question 11

distributive law
a(b + c)

Answer 11

ab + ac

Question 12

-(x + y)

Answer 12

= -x - y

Question 13

-(x - y)

Answer 13

-x + y

Question 14

7 - a(-5x + z)

Answer 14

7 + 5ax - az

Question 15

-3(x + 2y) - 4(x - y)

Answer 15

-7x - 2y

Question 16

5y - 2[3z - 2(y + 3z)]

Answer 16

9y + 6z

Question 17

Factorisation of algebraic expression

-20b + 15by - 10bz

Answer 17

5b(3y - 4 - 2z)

Question 18

factorise -6a - 24az - 4ay

Answer 18

-2a(3 + 12z + 2y)

Question 19

is n/2 = 1/2n?

Answer 19

yes

Question 20

is (n+1)/3 = 1/3(n + 1)?

Answer 20

yes

Question 21

is-1/3 from -1/3x an integer?

Answer 21

no. its a fractional coefficient

Question 22

simplify 1/2x - 1/9y - 1/8x + 11/3y

Answer 22

3/8x + 32/9y

Question 23

simplify 2/3 [2x - 5(x - 6y)]

Answer 23

20y - 2x

Question 24

express 1/3x + (2x - 5)/7 as a fraction in its simplest form

Answer 24

(13x - 15)/21

Question 25

express (2x - 5)/3 - 1/5(3x - 2) as a fraction in its simplest form

Answer 25

(x - 19)/15