lumone wrote:

If x and y are integers and y=|x+3|+|4-x| , does y=7?

(1) x<4

(2) x>-3

Remember that |a - b| is just the distance between a and b on the number line.

Write the question as:

y=|x - (-3)| + |4-x|

In words, this says: "y is equal to the distance from x to -3 plus the distance from x to 4. Draw a number line, draw the points -3 and 4, and put x in the middle. If you add the two distances, you clearly get 7, the distance from -3 to 4. If x is less than -3 or larger than 4, the sum of the distances will be larger than 7. Easy to see if you draw the picture. So we need both statements: C.

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