Question

What is the solution to 6x2 –14x ≥ –4? x is less than or equal to one third or x ≥ 2 x is greater than or equal to one third or x < 2 negative one third is less than x is less than 7 negative seven is greater than x is greater than one third

Answer 1

The inequality is given below as

`6x^2-14x\ge-4`

Step 1:

Take the constant to the other side

`\begin{gathered} 6x^(2)-14x\geqslant-4 \\ 6x^2-14x+4\ge0 \\ factorize \\ 6x^2-12x-2x+4\ge0 \\ 6x(x-2)-2(x-2)\ge0 \\ (6x-2)(x-2)\ge0 \end{gathered}`
`\begin{gathered} 6x-2\ge0,x-2\ge0 \\ 6x\ge2,x\ge2 \\ (6x)/(6)\ge(2)/(6),x\ge2 \\ x\leq(1)/(3),x\ge2 \end{gathered}`

Hence,

The final answer is

`\Rightarrow x\leqslant(1)/(3),x\geqslant2`

The FIRST OPTION is the right answer