Question

I need help with this equation this is a 5 part answer

Answer 1

We are given the following inequality

`(2x+1)(x-2)(3x-4)\leq0`

First, let us solve each factor.

`\begin{gathered} (2x+1)\leq0 \\ 2x+1-1\leq-1 \\ 2x\leq-1 \\ (2x)/(2)\leq-(1)/(2) \\ x\leq-(1)/(2) \end{gathered}`
`\begin{gathered} (x-2)\leq0 \\ x-2+2\leq2 \\ x\leq2 \end{gathered}`
`\begin{gathered} (3x-4)\leq0 \\ 3x-4+4\leq4 \\ 3x\leq4 \\ (3x)/(4)\leq(4)/(3) \\ x\leq(4)/(3) \end{gathered}`

Now, we have to merge the overlapping intervals

`(4)/(3)\leq x\leq2\;\;or\;\;x\leq-(1)/(2)`

Therefore, the solution of the given inequality is