Equation rules

Question 1

Addition

10x +2x =

Answer 1

10x +2x = 12x

Question 2

Order of operations

Answer 2

BRIDMAS

• First BRACKETS
• Then INDICES
• Then DIVISION OR MULTIPLICATION
• Then ADDITION OR SUBSTRACTION

Question 3

Addition

5x +3y + 10x=

Answer 3

5x+3y +10x=

5x+10x+ 3y=

15x +3y (we cannot simplify more)

Question 4

Subtraction

10x -3x=

Answer 4

10x -3x=
7x

Question 5

Subtraction

10x +3y -5x=

Answer 5

10x+3y-5x=
10x-5x+3y=
5x +3y

Question 6

Subtraction

10x+4xy - 2xy -11x=

Answer 6

10x + 4xy - 2xy - 11x=

You need to group the x and xy

10x -11x + 4xy- 2xy=
-x+2xy

Question 7

Multiplication

2x * 3x=

Answer 7

2x * 3x=

6x^2
(6 x to the power of 2)

You need to group the number and then the x

Question 8

Multiplication

3xy *4y^2

Answer 8

3xy * 4y^2=

12 x y^3
(12 x y to the power of 3)

Group number then the x and y

Question 9

Division

12x / 2

Answer 9

12 x / 2=
6x

group the numbers first then x

Question 10

Division

6xy / (2x)

Answer 10

6xy / (2x)=

3y (group the numbers first then the x and y)

Question 11

Division

12 (x^5) / [6 (x^3)]

Answer 11

12 (x^5) / [6(x^3)]=

2 x^2

Group the numbers first then the x

Question 12

96/4 - 4=

Answer 12

96/4 - 4= 24 - 4= 20

Question 13

36/9 + 1=

Answer 13

36/9 + 1= 4 +1 = 5

Question 14

(10-X) x 4 = 36

Answer 14

(10-X) x 4 = 36
(10 - x)= 36/4 = 9
10-9= x
1=x

Question 15

8+3 x 4- 6=

Answer 15

8+3 x 4- 6=
8 + 12 -6=
14

Question 16

(3+1)^2 x2 +5=

Answer 16

(3+1)^2 x2 +5=
4^2 x 2 + 5=
16 x 2 + 5=
32 + 5=
37

Question 17

160 / (3+7)=

Answer 17

160 / (3+7)=
160/ 10= 16

Question 18

(-3)^3 - (-2)^3 - square root (16)=

Answer 18

(-3)^3 - (-2)^3 - square root (16)=
-27 - (-8) - 4=
-27 +8 -4=
-23

Question 19

[(-3)^2 + (-2)^3]^2 + square root (27) - (-1)=

Answer 19

[(-3)^2 + (-2)^3]^2 + square root (27) - (-1)=
[9 -8]^2 +3 +1=
1^2 +3 +1=
1 +3+1= 5

Question 20

Write as an expression “I start with a number p and multiply it by 25 then I subtract 7 before dividing it by 3”

Answer 20

(25p-7)/3 =

Question 21

Write as an algebraic expression
The product of a and c is divided by b

Answer 21

(axc)/b= ac/b

Question 22

Simplify 3 y^2 + 4ab + 7y^2 +ab

Answer 22

3 y^2 + 4ab + 7y^2 +ab=
(3y^2 + 7y^2) + (4ab +ab)=
10 y^2 + 5ab

Question 23

Simplify 3q + 4pq - 2q +3qp + 4

Answer 23

3q + 4pq - 2q +3qp + 4=
(3q-2q) + 4pq +3qp +4=
q +7pq+4

Question 24

Multiplying expression
3a x 2b x 5c=

Answer 24

3a x 2b x 5c=
3x2x5xaxbxc=
30abc

Question 25

Multiplying expression 5d x e x 4d x e=

Answer 25

5d x e x 4d x e= 5x4 x e x d x e= 20 d e^2

Question 26

Multiplying expression 4 a^2 b c^2 x a^3b=

Answer 26

4 a^2 b c^2 x a^3b= 4 a^5bc^2

Question 27

Simplify 9x^2 / (8-5)^2 - 2x x 5x + 13x^2

Answer 27

9x^2 / (8-5)^2 - 2x x 5x + 13x^2= 9x^2 / 3^2 -10x^2 + 13x^2= 9 x^2 /9 +13x^2= x^2 + 13x^2= 14x^2

Question 28

Find x 2x +3 = 13

Answer 28

2x +3 = 13 2x = 13 -3= 10 x = 10/2 = 5

Question 29

Find x 4(x+2)=20

Answer 29

4(x+2)=20 (x+2)= 20/4=5 x=5-2=3

Question 30

Find w (w-25)/3 = -7

Answer 30

(w-25)/3 = -7 (w-25) = -7X3= -21 w= -21 +25 w= 4

Question 31

Find x x/6 - 2= -8

Answer 31

x/6 - 2= -8 x/6 = -8 +2= -6 x= -36