Solve 4x^2-8x-11-x^2+8x-16leq0

$$4 x ^ { 2 } - 8 x - 11 - x ^ { 2 } + 8 x - 16 \leq 0$$

Solve for x

$$x\in \begin{bmatrix}-3,3\end{bmatrix}$$

Solution Steps

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-8x-11+8x-16\leq 0$$

Combine -8x and 8x to get 0.

$$3x^{2}-11-16\leq 0$$

Subtract 16 from -11 to get -27.

$$3x^{2}-27\leq 0$$

Add 9 to both sides.

$$x^{2}\leq 9$$

Calculate the square root of 9 and get 3. Rewrite 9 as 3^{2}.

$$x^{2}\leq 3^{2}$$

Inequality holds for |x|\leq 3.

$$|x|\leq 3$$

Rewrite |x|\leq 3 as x\in \left[-3,3\right].

$$x\in \begin{bmatrix}-3,3\end{bmatrix}$$