Answer:
x<=-4 or -2<=x<=2 or x>=4
Step-by-step explanation:
First, you have to get the formula in its standard form,
x^4 - 18x^2 + 64 >= 0
Next, you factorise the expression as you would any trinomial. The fact that the degree of the inequality is 4 instead of 2 just adds an extra step,
(x^2 - 16)(x^2 - 4) >= 0
Get the zeroes/critical values of the equation by equating either bracket to zero.
x^2 - 16 = 0 and x^2 - 4 = 0
x^2 = 16 x^2 = 4
Since both values are positive, both answers are valid as squares of x. The aforementioned extra step is just square rooting these values. Remember: This means that both a positive and negative answer will arise from both equations.
x = 4 or x = -4 or x = 2 or x = -2
Now you have to show these values on a number line.
-4 -2 2 4
_|____|____|____|_
These are the critical values of the inequality, i.e. those values that make it equal zero (zeroes). Now to solve the inequality you need to substitute a value larger than 4 (called x big positive) and then a value between 2 and 4, between -2 and 2... until you sub a value less than -4 into the factorised expression. The point of this is to get the SIGN of the answer. As a rule, since no factors repeat themselves, after calculating x big positive you can simply alternate the signs going left. Try it out yourself!
+ -4 - -2 + 2 - 4 +
_|____|____|____|_
Since we're looking for values greater than or equal to zero, all critical values as well as "plus signs" will form part of the answer, namely:
x<=-4 or -2<=x<=2 or x>=4
P.S. If you prefer, you could also factorise each bracket further as both of them were DOTS brackets and you would have ended up with the same critical values.
