Factorise $5x - 15$ and $6 - 2x$. $$5x - 15 = 5(x - 3)$$ $$6 - 2x = 2(3 - x)$$ If $A$ and $B$ are variable quantities, we say that $A$ is proportional to $B$ if the fraction $ \frac{A}{B} $ is a constant. (b) Using your answers to part (a) above, show that $5x - 15$ is proportional to $6 - 2x$. (c) Is $x^2 + 3x + 2$ proportional to $2x + 2$? Justify your answer.

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Factorise $5x - 15$ and $6 - 2x$ - Junior Cycle Mathematics - Question Question 1 - 2015

Question Question 1

Factorise $5x - 15$ and $6 - 2x$. $$5x - 15 = 5(x - 3)$$ $$6 - 2x = 2(3 - x)$$ If $A$ and $B$ are variable quantities, we say that $A$ is proportional to $B$ if t... show full transcript

Worked Solution & Example Answer:Factorise $5x - 15$ and $6 - 2x$ - Junior Cycle Mathematics - Question Question 1 - 2015

Step 1

Factorise $5x - 15$ and $6 - 2x$

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Answer

$5x - 15 = 5(x - 3)$

$6 - 2x = 2(3 - x)$

Step 2

Show that $5x - 15$ is proportional to $6 - 2x$

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Answer

From part (a), we have:

$\frac{5x - 15}{6 - 2x} = \frac{5(x - 3)}{2(3 - x)}$

This simplifies to:

$\frac{5(x - 3)}{2(3 - x)} = \frac{5}{2} \text{ (constant value)}$

Thus, $5x - 15$ is indeed proportional to $6 - 2x$ .

Step 3

Is $x^2 + 3x + 2$ proportional to $2x + 2$? Justify your answer.

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Answer

Firstly, we need to factorise our two quantities:

$x^2 + 3x + 2 = (x + 1)(x + 2)$

$2x + 2 = 2(x + 1)$

Now, we divide one by the other:

$\frac{x^2 + 3x + 2}{2x + 2} = \frac{(x + 1)(x + 2)}{2(x + 1)} = \frac{x + 2}{2}$

This fraction is not constant since it depends on $x$ . Thus, the two quantities are not proportional.

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