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Graph the solution to the following inequality on the number line.(x+2)(x-7) greater than or equal to 0

User Eric Lin
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Solve the inequality:

(x + 2)(x - 7) ≥ 0

The product of x + 2 and x - 7 can only be 0 if any (or both) of the factors is 0.

The product can only be positive if both are positive or both are negative. These conditions can be expressed as:

x + 2 ≥ 0 and x - 7 ≥ 0

OR

x + 2 ≤ 0 and x - 7 ≤ 0

The first pair of conditions lead to:

x ≥ -2 and x ≥ 7

The combination of both conditions produces a single solution:

x ≥ 7

The second pair of conditions lead to:

x ≤ -2 and x ≤ 7

The combination of both conditions produces a single solution:

x ≤ -2

The total solution to the inequality is:

x ≤ -2 U x ≥ 7

U = Union

The graph of the solution is:

Graph the solution to the following inequality on the number line.(x+2)(x-7) greater-example-1
User Rick Pat
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