We are given the following inequality
[tex](2x+1)(x-2)(3x-4)\leq0[/tex]
First, let us solve each factor.
[tex]\begin{gathered} (2x+1)\leq0 \\ 2x+1-1\leq-1 \\ 2x\leq-1 \\ \frac{2x}{2}\leq-\frac{1}{2} \\ x\leq-\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} (x-2)\leq0 \\ x-2+2\leq2 \\ x\leq2 \end{gathered}[/tex][tex]\begin{gathered} (3x-4)\leq0 \\ 3x-4+4\leq4 \\ 3x\leq4 \\ \frac{3x}{4}\leq\frac{4}{3} \\ x\leq\frac{4}{3} \end{gathered}[/tex]
Now, we have to merge the overlapping intervals
[tex]\frac{4}{3}\leq x\leq2\;\;or\;\;x\leq-\frac{1}{2}[/tex]
Therefore, the solution of the given inequality is
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