Inequation query

Check out this video on my YouTube channel: https://youtu.be/PWsUOe77__E

It discusses how to handle various inequalities with multiple factors.

GMAT Club's solution correctly says −5<x<3. I think you've just copied incorrectly.

Dear ir2pid

In questions like the one you posted, the Wavy Line Method is an elegant and quick way to find the range of x.

Here is what you do in the Wavy Line Method:

1. Express the given expression in standard factorized form, that is in the form:

\((x-a)^{p}(x-b)^{q}\) < or > 0

The inequality you presented above is already in factorized form.

But is it in Standard form? Not yet. [because one of the factors is (3-x). We need to convert it to the form (x-3)]

Let's multiply both sides of the inequality with -1. Note that multiplying both sides of an inequality with a negative number changes the sign of inequality. So, we get:

(x+5)(x-3) < 0

2. Plot the Zero Points on the number line. These are the points for which the factorized expression becomes equal to zero.

(x+5)(x-3) becomes equal to zero for x = -5 and x = 3. So, these are the zero points. Plot them on the number line.

3. Now, starting from the TOP RIGHT CORNER of the number line, draw a Wavy Line that passes through these zero points.

The parts where this wavy line is ABOVE the number line are the parts where the given expression will be positive.
The parts where this wavy line is BELOW the number line are the parts where the given expression will be negative.

That's it!



From the Wavy Line we've drawn for your inequality, you can easily see that that the expression (x+5)(x-3) will be negative for -5 < x < 3

Practice the Wavy Line Method for one or two more questions and am sure you'll start finding questions like this one to be pretty easy.

Hope this was useful!

Japinder

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