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Find the value of seven 𝑥 given one over five plus 𝑥 over seven equals 14 over 70.
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So here, we’ve got a fairly simple equation that we’ve got to solve using a bit of linear algebra, but it involves fractions.
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So we do need to be a little bit careful.
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So a fifth plus 𝑥 over seven equals 14 over 70.
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So I think the first thing that I’m gonna do is simplify that fraction on the right-hand side.
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Well, I know that sevens go into 14 twice and sevens go into 70 10 times.
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But even that will simplify down further because twos go into two once and twos go into 10 five times.
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So 14 over 70 is the same as one over five.
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So simplifying the fraction on the right-hand side, gives us that.
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Now I want to get that 𝑥 on its own, so I’m going to subtract this a fifth from both sides.
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And if I subtract a fifth from the left-hand side, then I’m just left with 𝑥 over seven.
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And if I subtract a fifth from the right-hand side, a fifth minus a fifth is nothing.
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So 𝑥 over seven is equal to zero.
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Now if I multiply both sides by seven, on the left-hand side, seven times 𝑥 over seven is just 𝑥.
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And on the right-hand side, seven times zero is zero.
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So 𝑥 is equal to zero.
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But the question, remember, asked us to find the value of seven 𝑥.
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So I need to multiply this answer by seven.
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And seven times zero is zero, so seven 𝑥 is also equal to zero.
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And there we have it, seven 𝑥 is equal to zero.