How many integers will satisfy the inequality x + 4 |x + 10|?

Question

How many integers will satisfy the inequality x + 4 > |x + 10| ?

A. 10
B. 8
C. 5
D. 2
E. 0

Source : Wizako

chetan2u · Accepted Answer

x+4>|x+10| As both sides are positive, square the two sides x^2+8x+16>x^2+20x+100…….12x<-84…….x<-7 But whenever x<-7, the left hand side x+4 is negative and cannot be greater than a MOD. Hence the answer is 0. E

gmatophobia · Answer

Case 1 : x < -10

x + 4 > - (x-10)

2x > -14

x > -7

As x < -10; there is no value in this region for which the inequality will hold true

Case 2 : x >= -10

x + 4 >= x + 10

4 >= 10

Invalid region.

Hence there is no value for x for which the inequality hold true.

Answer E

mikhailhx1 · Answer

Why are we assuming in case 1 and case 2 that x<-10 and x>=-10? since this hasn't been stated in the question

gmatophobia · Answer

Hey  mikhailhx1

We are checking this range to apply the following logic -

|a| = a →  a \geq 0 
|a| = -(q) →  a< 0

Hence, in this example

|x - 10| = (x-10) →  x - 10 \geq 0

|x - 10| = -(x-10) →  x - 10 < 0

Rikhraj1 · Answer

Bunuel   bb  can u pls help me with this question.

Bunuel · Answer

How many integers will satisfy the inequality x + 4 > |x + 10| ?

A. 10
B. 8
C. 5
D. 2
E. 0

The right-hand side of the inequality, |x + 10|, is an absolute value, which is always non-negative. For the left-hand side, x + 4, to be greater than the right-hand side, it must then be positive. This gives x + 4 > 0, which simplifies to x > -4.

Additionally, since x > -4, it follows that x + 10 > 0. This means |x + 10| = x + 10. Substituting this into the inequality gives:

x + 4 > x + 10
4 > 10

This is clearly false. Therefore, the given inequality has no solutions.

Answer: E

How many integers will satisfy the inequality x + 4 > |x + 10|?

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