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How many integers will satisfy the inequality x+4 > |x+10| ?
- a)10
- b)8
- c)5
- d)2
- e)0
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
How many integers will satisfy the inequality x+4 > |x+10| ?a)10b)8...
To find the number of integers that satisfy the inequality x + 4 > |x + 10|, we can analyze the different cases based on the absolute value function.
Case 1: x + 10 ≥ 0 When x + 10 is non-negative, the absolute value |x + 10| can be written without the absolute value signs. Thus, the inequality becomes: x + 4 > x + 10
By subtracting x from both sides, we get: 4 > 10
This inequality is false, so there are no solutions in this case.
Case 2: x + 10 < 0 When x + 10 is negative, the absolute value |x + 10| becomes the negation of the expression inside the absolute value signs. Thus, the inequality becomes: x + 4 > -(x + 10)
Simplifying the inequality, we have: x + 4 > -x - 10
By adding x to both sides, we get: 2x + 4 > -10
Next, by subtracting 4 from both sides, we have: 2x > -14
Finally, dividing both sides by 2 gives: x > -7
This inequality means that x must be greater than -7. Since we are looking for integers, we can see that there are no integers greater than -7 that satisfy this condition.
Therefore, combining both cases, we find that there are no integers that satisfy the inequality x + 4 > |x + 10|. Hence, the answer is E: 0.
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How many integers will satisfy the inequality x+4 > |x+10| ?a)10b)8...
The inequality x < 4="" means="" that="" x="" can="" take="" on="" any="" value="" less="" than="" 4.="" since="" x="" is="" an="" integer,="" the="" integers="" that="" satisfy="" the="" inequality="" are="" -3,="" -2,="" -1,="" 0,="" 1,="" 2,="" and="" 3.="" therefore,="" there="" are="" 7="" integers="" that="" satisfy="" the="" inequality.="" 4="" means="" that="" x="" can="" take="" on="" any="" value="" less="" than="" 4.="" since="" x="" is="" an="" integer,="" the="" integers="" that="" satisfy="" the="" inequality="" are="" -3,="" -2,="" -1,="" 0,="" 1,="" 2,="" and="" 3.="" therefore,="" there="" are="" 7="" integers="" that="" satisfy="" the="" />
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How many integers will satisfy the inequality x+4 > |x+10| ?a)10b)8c)5d)2e)0Correct answer is option 'E'. Can you explain this answer?
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