Loading [MathJax]/jax/output/SVG/jax.js
 
+0  
 
0
32
1
avatar+1782 

Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.

 Aug 12, 2024
 #1
avatar+1950 
+1

We don't have the expand everything, as we can just use factoring to our advantage. 

Moving all terms to the right side of the equation, we get

(x2)(x+6)(x2)(x+5)0

 

Now, since both terms have x- 2, we can factor it out to get

(x2)(x+6(x+5))0(x2)(x+6x5)0x20

 

Isolating x from the equation, we get

x2

 

In interval notation, this is (,2]

 

Thanks! :)

 Aug 12, 2024
edited by NotThatSmart  Aug 12, 2024

0 Online Users