THE X FILES
What is the HCF of 18x and 24x?
6x
Simplify:
7x+4x−3x
8x
Escape the equation:
x+17=29
x = 12
What comes next?
7, 12, 17, 22, ?
27
A number increased by 13 is 31.
Find the number.
18
The expression below has one hidden common factor. Find it and factorise completely:
12x+18
6(2x +3)
Simplify:
8a+3b−5a+2b
3a + 5b
Escape:
5x−8=27
x = 7
Find the next two terms:
31, 27, 23, 19, …
15, 11
A notebook costs ₹20 more than a pen.
Together they cost ₹140.
How much does each cost?
Pen = ₹60, Notebook = ₹80
Factorise:
15xy−10x
5x(3y - 2)
Simplify:
4(2x+3)−5x
3x + 12
The variable is hiding on both sides:
7x+4=3x+28
Find xx.
x = 6
A pattern begins:
5, 8, 11, 14,…
Let nn be the position number and tt the term.
Find a general rule connecting nn and tt.
t = 3n + 2
The sum of three consecutive integers is 72.
Find all three integers.
23, 24, 25
Find the HCF of all three terms:
18x2y,30xy2,42xy
6xy
Simplify:
3(2x−5)−2(x+4)+7
4x - 16
This one has brackets:
4(x−3)=2x+10
Find xx.
x = 11
A sequence is:
7, 12, 17, 22,…
A student claims that the general rule is:
t=5n+2
Is the rule correct? Prove your answer using substitution.
For n=1:
5(1)+2=7
For n=4:
5(4)+2=22
Therefore the rule works for the given terms.
A number is multiplied by 5 and then 7 is added. The result is the same as three times the number plus 25.
Find the number.
x = 9
Mahir claims:
12x2+18x=6x(2x+3)
Aashrey claims:
12x2+18x=3x(4x+6)
Both expressions are correct. Which one is completely factorised, and how can you prove it?
Mahir is right!
The second answer can be factorised further because 4x+64x+6 has a common factor of 2.
Simplify:
5(2x−3)−3(1−x)+2(4−x)
11x - 10
Solve:
−2(4−x)=6(x+2)+3x
x = -20/7
A sequence follows this rule:
4, 9, 14, 19, …
What is the 20th term?
99
Why: The pattern increases by 5, so
t=5n−1Three consecutive odd integers have a sum of 81. Find them.
25, 27, 29