Solve the inequations: 3 x+1 6 x-4 - Vidyadip

Question

Solve the inequations: $3 \mathrm{x}+1 \geq 6 \mathrm{x}-4$

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Answer

$
3 x+1 \geq 6 x-4
$
Subtracting $3 x$ from both sides, we get
$
1 \geq 3 \mathrm{x}-4
$
Adding 4 on both sides, we get
$
5 \geq 3 x
$
Dividing by 3 on both sides, we get
$
\frac{5}{3} \geq x
$
i.e., $x \leq \frac{5}{3}$
i.e, $x$ takes all real values less than or equal to $\frac{5}{3}$. $\therefore$ the solution set is $\left(-\infty, \frac{5}{3}\right]$

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