Simultaneous Inequality

Algebra Level 4

What is the number of integer solutions of the following simultaneous inequalities: x + 2 x 2 − 4 x + 3 ≥ 0 , 9 x − 8 ≤ − 1 ? \frac{x+2}{x^2-4x+3}\geq0, \frac{9}{x-8}\leq-1?

7 8 5 6

Sandeep Mehra by Sandeep Mehra , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tom Engelsman
Aug 15, 2018

The first inequality holds true for x ∈ [ − 2 , 1 ) ∪ ( 3 , ∞ ) x \in [-2, 1) \cup (3, \infty) . The second one holds true for x ∈ [ − 1 , 8 ) x \in [-1, 8) . Hence, the required solution that satisfies BOTH inequalities is x = [ − 1 , 1 ) ∪ ( 3 , 8 ) x = [-1, 1) \cup (3, 8) with 6 \boxed{6} total solutions in x ∈ Z . x \in \mathbb{Z}.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...