Question
Solve the inequality 3(x – 1) $\leq$ 2 (x – 3) for real x.
✓
Answer
It is given in the question that,
3(x – 1) $\leq$ 2 (x – 3)
$\Rightarrow$ 3x – 3 $\leq$ 2x – 6
$\Rightarrow$ 3x – 3+ 3 $\leq$ 2x – 6+ 3
$\Rightarrow$ 3x $\leq$ 2x – 3
$\Rightarrow$ 3x – 2x $\leq$ 2x – 3 – 2x
$\Rightarrow$ x $\leq$ -3
$\therefore$ The solutions of the given inequality are defined by all the real numbers less than or equal to -3.
Thus, the solutions set to the given inequality are (-$\infty $, - 3]
3(x – 1) $\leq$ 2 (x – 3)
$\Rightarrow$ 3x – 3 $\leq$ 2x – 6
$\Rightarrow$ 3x – 3+ 3 $\leq$ 2x – 6+ 3
$\Rightarrow$ 3x $\leq$ 2x – 3
$\Rightarrow$ 3x – 2x $\leq$ 2x – 3 – 2x
$\Rightarrow$ x $\leq$ -3
$\therefore$ The solutions of the given inequality are defined by all the real numbers less than or equal to -3.
Thus, the solutions set to the given inequality are (-$\infty $, - 3]
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