Question

Solve each inequality. Round to the nearest hundredth. 3x2 – 4 ≤ 6 – 5x

Answer 1

Answer:

$x\in[-2.84,1.17]$

Step-by-step explanation:

The first, we will write our inequality in another form:

$3x^2-4\leq 6-5x$

$3x^2-4-6+5x\leq 0$

$3x^2+5x-10\leq 0$

We want to know when is it equal to 0.

First we solve the equation $3x^2+5x-10=0$:

$x_{1,2}=\frac{-5+-\sqrt{25+120}}{6}$

$x_{1,2}=\frac{-5+-12.04}{6}$

$x_1=1.17$

$x_2=-2.84$

So we want to know when $3x^2+5x-10\leq 0$ is true. We know, when a>0 function is negative when x is between two zeros. In our example a=3>0. Then we have:

It is true if $x\in[-2.84,1.17]$