Answered By Jonny C

This is called a Quadratic Inequality.

Ask yourself, what value of x would give a solution that's greater than zero?

For example, if x = 1, you'd have (1+144)(1+67) = 9860, which is greater than zero, however, if x = -80, you'd have (-80+144)(-80+67) = -832, which is lesser than zero. So what are all the values of x that would give you a solution greater than zero?

First solve by finding the zeros of this quadratic equation. This step is simple since the equation is already factored. 0 = (x+144)(x+76), x = -144, -67

If x is either of these numbers, it would give you zero. So what if x is greater than -67? Let's try -66

(-66+144)(-66+67) = 78 which is greater than zero. So this means any number greater than -67 would be give you a solution greater than zero.

So is the answer x > -67? Well that's only one half of the answer. Recall that two negative numbers multiply to give you a positive number. So this is where the other zero comes into play. For example, if x = -145, then we have (-145+144)(-145+67) = 78, which is also greater than zero. So any number smaller than -144 would also produce an answer greater than zero.

So the solution is x > -67 or x < -144. But in inequalities, we express out answers as such, (-∞, -144) U (-67, ∞), all this means is that x must be between negative infinity and -144 (ie. a smaller number than -144) OR (which is denoted by 'U') x must be between -67 and positive infinity (ie. a larger number than -67). Side note- we use rounded brackets to exclude the number, meaning that -144 and -67 is not included in the solutions for x since it must be greater than zero, not greater than or equal to zero. Square brackets would be used if -144 and -67 is part of the solution.

Answered By Majid B

According to the following sign table, the solution is:

 {x|x<-144 or x>-67}