Solve the following system of equations in R- -3 x-4-2- -5-12

We have, | 3x 4/2 | ≤5/12≤ 0 Case I:When | 3x 4 |≥ 0 | 3x 4/2 | 5/12≤ 0 ⇒ | 3x 4/2 | 5/12≤ 0 ⇒3x 4/2 5/12≤ 0 ⇒6(3x 4) 5/12≤ 0 ⇒ 18x 24 5≤ 0 ⇒ 18x 29≤ 0 ⇒ 18 ...

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Standard XII

Mathematics

Inequalities Involving Modulus Function

Solve the fol...

Question

Solve the following system of equations in R.
$∣ ∣ \frac{3 x - 4}{2} ∣ ∣ \leq \frac{5}{12}$

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Solution

We have,

$∣ ∣ \frac{3 x - 4}{2} ∣ ∣ \leq \frac{5}{12} \leq 0 C a s e I : W h e n | 3 x - 4 | \geq 0 ∣ ∣ \frac{3 x - 4}{2} ∣ ∣ - \frac{5}{12} \leq 0 \Rightarrow ∣ ∣ \frac{3 x - 4}{2} ∣ ∣ - \frac{5}{12} \leq 0 \Rightarrow \frac{3 x - 4}{2} - \frac{5}{12} \leq 0 \Rightarrow \frac{6 (3 x - 4) - 5}{12} \leq 0 \Rightarrow 18 x - 24 - 5 \leq 0 \Rightarrow 18 x - 29 \leq 0 \Rightarrow 18 x \leq 29 \Rightarrow x \leq \frac{29}{18} . . . (i i)$

$C a s e I I : W h e n | 3 x - 4 | < 0 ∣ ∣ \frac{3 x - 4}{2} ∣ ∣ - \frac{5}{12} \leq 0 - 6 (3 x - 4) - 5 \leq 0 - 18 x + 24 - 5 \leq 0 - 18 x + 19 \leq 0 - 18 x \leq - 19 18 x \geq - 19, x \geq \frac{19}{8} . . . (i i i) Combining~(ii)~and~(iii)~to get solutions set as (\frac{19}{18}, \frac{29}{18})$

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