Solve This Inequality?

Question

x(x-2)(x+1)(x+5) ≥ 0

I simply do not understand this question.

I guess that they're asking for the answer:

x ≥ 0
x ≥ 2
x ≥ -1
x ≥ 5

Answer 1

u have 4 tems multiplied by each other .. the inequlity will be true as long as the number of the negative sign terms is even.
i. for x< -5 all terms are negative .. so their product is ≥0
ii. at x=-5 the LHS=0
iii. for -5 iv. for x=-1 LHS=0
v. for -1 vi. for x=0 LHS=0
vii. for 0 viii. for x=2 LHS=0
ix. for x>2 all terms are positive so the product is positive

i.e. the solutiom is:

x<=-5, -1<=x<=0, x ≥ 2

Answer 2

Hi,

While solving such inequalities, you are not expected to solve for exact values of x, instead the answers will be another inequality or bound, such as x ≥ n, etc.

Here the inequality is given as,
x(x-2)(x+1)(x+5) ≥ 0
That means the inequality is either positive or 0.

if we substitute a bound for x, it should satisfy or solve the equation. There are 4 bounds given, we have to examine whether they satisfy the inequality.

x ≥ 0, fails inequality for the non-zero positive values of x ,which are less than 2, as (x -2) becomes negative and thereby the inequality turns negative. Note that x = 0 satisfies the inequality, as x is a factor.

x ≥ 2, satisfy the inequality in its entire range starting from x = 2 or greater than 2,. At x = 2, (x -2) = 0 and the inequality is satisfied. For non-zero positive values of x greater than 2 all the factors are positive and the inequality is positive. Therefore, x ≥ 2 satisfies the inequality.

x ≥ -1. This includes, in itself, the range x ≥ 0. we have already examined x ≥ 0, which fails the inequality. So x ≥ -1 fails the inequality for the same reason. However the negative values of x greater than or equal to -1, satisfy the equation, but not the entire range x ≥ -1.

x ≥ 5. This is included in the range x ≥ 2, which satisfies the inequality. So x ≥ 5, also satisfies the inequality.

However the solution for the values of x that satisfy the values are given by the following.
x ≤ -5
-1 < x < 0 (includes both -1 and 0)
x ≥ 2

Hope this meets your need. Otherwise post the original question verbatim.

Good luck

Answer 3

The answer is x < or equal -5
-1 <(or equal) x <(or equal) 0
x > or equal 2

Answer 4

x>=0
x>=2
x<=-1
x<=-5