WEBVTT
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A number machine is shown.
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Part a) Calculate the output when the input is nine.
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Part b) Calculate the output when the input is negative nine.
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The number machine has two steps to get from the input to the output, firstly subtracting one and secondly multiplying by four.
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In part a), weβre told that the input is nine.
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Subtracting one from nine gives us an answer of eight.
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Multiplying eight by four is 32.
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This means that when the input is nine, the output from the number machine is 32.
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Part b) asks us to calculate the output when the input is negative nine.
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Subtracting one from negative nine gives us negative 10.
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Subtracting a number from a negative number takes us further down our number line.
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We then need to multiply negative 10 by four.
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Multiplying a negative number by a positive number gives us a negative answer.
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And 10 multiplied by four is equal to 40.
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Therefore, negative 10 multiplied by four is equal to negative 40.
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When the input to the number machine is negative nine, then its output is negative 40.
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Whilst we are not asked to in this case, we could write the output π¦ as an expression in terms of the input π₯.
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The first step in our number machine is to subtract one.
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Therefore, we would have π₯ minus one.
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We then multiply this answer by four, π₯ minus one multiplied by four.
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This is usually written with a four in front of the bracket.
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So we have four multiplied by π₯ minus one.
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The output π¦ in this question is equal to four multiplied by π₯ minus one.
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We could then use this to work out the output when we are given any input π₯.