What relation do you see between a number and its absolute value?
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Well, since the absolute value of a single number is its distance from zero, the sum of the absolute values of two numbers is not the distance between them, it's the sum of each number's distance from zero.
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ᴛʜᴇ ϙᴜɪᴄᴋ ᴡᴀʏ ᴛᴏ ᴛʜɪɴᴋ ᴀʙᴏᴜᴛ ᴀʙsᴏʟᴜᴛᴇ ᴠᴀʟᴜᴇs ɪs ᴛʜᴀᴛ ᴛʜᴇ ᴀʙsᴏʟᴜᴛᴇ ᴠᴀʟᴜᴇ ᴏғ ᴀ ɴᴜᴍʙᴇʀ sɪᴍᴘʟʏ ᴛᴇʟʟs ʏᴏᴜ ʜᴏᴡ ғᴀʀ ᴀᴡᴀʏ ɪᴛ ɪs ғʀᴏᴍ ᴢᴇʀᴏ ᴏɴ ᴛʜᴇ ɴᴜᴍʙᴇʀ ʟɪɴᴇ. ғᴏʀ ᴇxᴀᴍᴘʟᴇ, sɪɴᴄᴇ ᴛʜᴇ ɴᴜᴍʙᴇʀs 5 ᴀɴᴅ –5 ᴀʀᴇ ʙᴏᴛʜ 5 sᴛᴇᴘs ᴀᴡᴀʏ ғʀᴏᴍ ᴢᴇʀᴏ ᴏɴ ᴛʜᴇ ɴᴜᴍʙᴇʀ ʟɪɴᴇ, ᴛʜᴇʏ ʙᴏᴛʜ ʜᴀᴠᴇ ᴛʜᴇ sᴀᴍᴇ ᴀʙsᴏʟᴜᴛᴇ ᴠᴀʟᴜᴇ ᴏғ 5.
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