According to the question,
The inequalities given are,
3x – 7 > 2(x – 6) and 6 – x > 11 – 2x
3x – 7 > 2(x – 6)
⇒ 3x – 7 > 2x – 12
⇒ 3x – 2x > 7 – 12
⇒ x > -5 ………… (i)
6 – x > 11 – 2x
⇒ 2x – x > 11 – 6
⇒ x > 5 ……….(ii)
From equations (i) and (ii),
We can infer that the solution of given inequalities is (5, ∞).
Solve each of the following in equations and represent the solution set on the number line \( \dfrac{5x}{4}-\dfrac{4x-1}{3}>1,\) where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line.\( \dfrac{5x-8}{3}\geq \dfrac{4x-7}{2}\), where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9, where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6, where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line. 5x + 2 < 17, where
(i) x ϵ Z,
(ii) x ϵ R.