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Two numbers, 𝑎 and 𝑏, are opposite one another. If 𝑎 is 3 units to the right of 8 on a number line, determine the value of 𝑏.

Two numbers 𝑎 and 𝑏 are opposite one another. If 𝑎 is three units to the right of eight on a number line, determine the value of 𝑏.

We can start by sketching a number line, putting zero in the middle. We can also go ahead and add the number eight. Our problem tells us that the letter 𝑎 is three units to the right of eight. Three units to the right of eight is 11.

𝑏 is the opposite of 𝑎. 𝑎 is 11 units to the right of zero. The opposite of that would be 11 units to the left of zero. Numbers to the left of zero on a number line are negative. 11 units to the left of zero on a number line is negative 11. 𝑏 is equal to negative 11.

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