# How do you solve 2x^2-3<=x?

Oct 6, 2016

X

#### Explanation:

$2 {x}^{2} - 3 \le x$
Think $2 {x}^{2} - 3 = x$
$2 {x}^{2} - x - 3 = 0$
Factorise
$\left(2 x - 3\right) \left(x + 1\right) = 0$
So actually
$\left(2 x - 3\right) \left(x + 1\right) \le 0$
When you do this make sure you keep everything on the right sides
Now sketch the graph. Yes please do that!!
It is bucket shaped and crosses the x axis at $\frac{3}{2}$ and -1
So for the values to be less than or equal to 0, x must be greater than or equal to -1 and less than or equal to $\frac{3}{2}$

$- 1 \le x \le \frac{3}{2}$

Oct 6, 2016

Sorry $- 1 \le x \le \frac{3}{2}$