Answer: Overall, Alex lost 7 pounds
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Explanation:
Draw a vertical number line. Let's say we start at 0 on the number line. Zero means no net change (he doesn't gain weight, nor does he lose weight either).
Losing 8 pounds means we go down 8 units. Think of it like being at the ground level and then going down 8 floors to the basement level of a large building (eg: parking garage maybe).
After this movement, we're at -8 on the number line. Then move up 9 units to arrive at +1 or just 1 on the number line. So Alex has gained those 8 pounds back to his original weight, plus an extra pound. So that's why -8+9 = 1.
Then move down 2 units to get to -1. Lastly, from -1 move 6 units down to get to -7.
So overall, Alex has lost 7 pounds when everything is said and done.
Refer to the diagram below. We start at point A, move to point B after losing 8 pounds, then to C when gaining 9 pounds, and so on until we get to point E. Point E is at -7 on the vertical number line to represent that he lost 7 pounds.
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We can think of it in another way:
add up all the losses to get
loss of 8 + loss of 2 + loss of 6 = loss of 16
So he lost 16 pounds if we ignore the "gained 9 pounds", but we have to account for that. So we'll take 9 away from 16 to get 16-9 = 7.
Overall, Alex lost 7 pounds.
