Question

. Solve: |x - 5| ≤ |2x + 11|.​

Answer 1

☆Answer☆

Solution

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Given, P={x : 5<2x−1≤11,x∈R} and Q={x : −1≤3+4x<23,x∈I}

Solving for P,

5<2x−1≤11

⇒5+1<2x≤11+1

⇒6<2x≤12

⇒3<x≤6

Hence, P={x : 3<x≤6,x∈R}

The solution P is represented on number line (a).

Next, solving for Q

−⇒1≤3+4x<23

⇒−1−3≤4x<23−3

⇒−4≤4x<20

⇒−1≤x<5

As Q∈I

Hence, solution Q={−1,0,1,2,3,4}

The solution Q is represented on number line (b).

Therefore, P∩Q={4}

Answer 2

Answer:

If  |x - 5| ≤ |2x + 11|  then x≤  16

Step-by-step explanation:

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign.

|x - 5| ≤ |2x + 11|

|x -2x- 5| ≤ | 11|

|x -2x | ≤ |11 + 5|

| -x | ≤ |16|

x ≤  16