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

Solution:

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 \\ \frac{6x}{6}\ge\frac{2}{6},x\ge2 \\ x\leq\frac{1}{3},x\ge2 \end{gathered}$

Hence,

The final answer is

$\Rightarrow x\leqslant\frac{1}{3},x\geqslant2$

The FIRST OPTION is the right answer