find-the-range-or-ranges-of-value-x-can-take-for-x-6-gt-2x-3-

Question Number 10777 by j.masanja06@gmail.com last updated on 24/Feb/17

find the range or (ranges) of value x

can take for x + 6 > [2 x + 3]

Commented by mrW1 last updated on 24/Feb/17

d o y o u m e a n x + 6 >∣ 2 x + 3 ∣ ?

Commented by j.masanja06@gmail.com last updated on 25/Feb/17

yes!

Answered by mrW1 last updated on 24/Feb/17

i f 2 x + 3 ⩾ 0, i . e . x ⩾ - \frac{3}{2}

x + 6 > 2 x + 3

x < 3

\Rightarrow - \frac{3}{2} ⩽ x < 3

i f 2 x + 3 < 0, i . e . x < - \frac{3}{2}

x + 6 > - 2 x - 3

3 x > - 9

x > - 3

\Rightarrow - 3 < x < - \frac{3}{2}

\Rightarrow r a n g e o f x :

- 3 < x < 3

Answered by lee last updated on 25/Feb/17

s o l 1) {(x + 6)}^{2} > {(2 x + 3)}^{2}

3 x^{2} - 27 < 0, - 3 < x < 3

s o l 2)

i) x ≧ - \frac{3}{2}, x + 6 > 2 x + 3

- \frac{3}{2} ≦ x < 3

i i) x < - \frac{3}{2}, x + 6 > - 2 x - 3

- 3 < x < - \frac{3}{2}

∴ i) \cup i i) \to - 3 < x < 3

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