Solve the inequality: 2 3x – 4 5 - Vidyadip

Question

Solve the inequality: 2 $\le$ 3x – 4 $\le$ 5

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Answer

Given inequality 2 $\le$ 3x – 4 $\le$ 5
$\Rightarrow$ 2 $\le$ 3x – 4 $\le$ 5
$\Rightarrow$ 2 + 4 $\le$ 3x – 4 + 4 $\le$ 5 + 4
$\Rightarrow$ 6 $\le$ 3x $\le$ 9
$\Rightarrow$ 6/3 $\le$ 3x/3 $\le$ 9/3
$\Rightarrow$ 2 $\le$ x $\le$ 3
$\therefore$ all real numbers x greater than or equal to 2 but less than or equal to 3 are a solution of given equality.
x $\in$ [2, 3] solution set = [2,3]

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