Factorise $5x - 15$ and $2x - 6$.
If A and B are variable quantities, we say that A is proportional to B if the fraction \( \frac{A}{B} \) is a constant.
Worked Solution & Example Answer:Factorise $5x - 15$ and $2x - 6$ - Junior Cycle Mathematics - Question 2 - 2015
Step 1
Factorise $5x - 15$
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Answer
To factorise 5x−15, we can factor out the greatest common factor, which is 5:
5x−15=5(x−3)
Step 2
Factorise $2x - 6$
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Answer
Similarly, for 2x−6, we factor out the greatest common factor, which is 2:
2x−6=2(x−3)
Step 3
Show that $5x - 15$ is proportional to $2x - 6$
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Answer
From part (a), we can express the factors:
We found:
5x−15=5(x−3)
2x−6=2(x−3)
Now, to show proportionality, we take the ratio:
2(x−3)5(x−3)=25
Since this fraction is a constant, it proves that 5x−15 is proportional to 2x−6.
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