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