Chapter 6.1, Problem 76STP

To determine

To find: The inequality of the equation $2x^2-12\le -5x$ .

Answer to Problem 76STP

The inequalities of the equation are $x\le \frac{3}{2}$ or $x\le -4$ .

Explanation of Solution

Given information:

The given equation is $2x^2-12\le -5x$ .

Calculation:

Calculate the inequality of the equation.

  $2x^2-12\le -5x$

Adding both sides by $5x$ .

  $\begin{array}{l}2x^2-12+5x\le -5x+5x\\ 2x^2-12+5x\le 0\end{array}$

Now, using the method term splitting to further solve equation.

  $\begin{array}{c}2x^2+5x-12\le 0\\ 2x^2+8x-3x-12\le 0\\ 2x(x+4)-3(x+4)\le 0\\ (2x-3)(x+4)\le 0\end{array}$

That is,

  $(2x-3)\le 0$ or $(x+4)\le 0$

So,

  $x\le \frac{3}{2}$ or $x\le -4$

Therefore, the inequalities of the equation are $x\le \frac{3}{2}$ or $x\le -4$ .