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

Question

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

1) x -3

Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/

ugimba · Answer

Case 1: x < 4 substitute x = 3 in the equation. you get y = |3+3| + |4-3| = 6 + 1 = 7 sufficient. substitute x = -7 you get y = |-7+3| + | 4-(-7)| = |-3|+|11| = 3+ 11 = 14 insufficient. Case 2: x > -3 substitute x = -1, you get y = |(-1)+3|+|4-(-1)| = |2|+|4+1| = 7. sufficient. substitute x = 8, you get y = |8+3|+|4-8| = |11|+|-4| = 11+4 = 15 insufficinet. together x<4 and x > -3 ... you get sufficient ... So answer should be C.

peraspera · Answer

1. x=-6
y=|-6+3|+|4+6|=13
insuff.

2. x=20
 |20+3|+|4-20|=39
insuff.

combine 1) and 2) - the range is -2,-1,0,1,2,3
trying x for any from this range will result in 7
suffic.

Economist · Answer

Answer should be B. What is OA?

here we have three distinct regions: 
1) x 4

For 1), x+3 is -ve and 4-x is positive, so the eq becomes,
 y = -3-x+4-x = 1-2x >> no solution

For 2), x+3 is +ve and 4-x is positive,
 y = x+3+4-x = 7 >> this range is true.

For 3), x+3 is +ve and 4-x is positive,
 y = 7.

Hence, y = 7 for all x>-3.

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

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