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How might you solve equations in this new system? Note 7
Let's start with the equation 3x = 8. Looking at the multiplication table, we can see that 3 * 6 = 8, so x = 6 is a solution. In fact, it's the only solution, because there is only one "8" in the third row of the multiplication table.
Or you could reason like this: "To solve 3x = 8 in our regular system, I would divide both sides by 3. That's the same as multiplying by the reciprocal of 3. In this system, 3 * 7 = 1, so 7 is the reciprocal of 3."
So you can calculate as follows:
3x = 8
7(3x) = 7 * 8
(7 * 3)x = 6 (Note that in the table, 7 * 8 = 6)
x = 6
Multiplying by 7 is the equivalent of dividing by 3 in this system. If you need to subtract, you can add the opposite of a number.
If you needed to solve the equation x + 4 = 2, you could reason like this: "To solve x + 4 = 2, I want to subtract 4 from both sides. In this system, 6 is the opposite of 4, so I can add 6 to both sides in order to remove the 4."
You would calculate as follows:
x + 4 = 2
x + (4 + 6) = 2 + 6
x + 0 = 8
x = 8
Try to solve these equations. If you have trouble, you can always use the operations table.
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