The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between
Bunuel, can you please explain this one?  Choose one:  A) 0 and 0.5  B) 0.5 and 1  C) 1 and 1.5  D) 1.5 and 2  E) 2 and 2.5
Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5&gt;4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).   Try x=1 --&gt; LHS=3^5=81*3= 
<gadget id="calculator">81*3</gadget>
<output>243</output>
243 and RHS=4^4=64*4= 
<gadget id="calculator">64*4</gadget>
<output>256</output>
256, so (1 + 2x)^5 &lt; (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5= (1 + 3x)^4 is slightly more than 1.   Answer: 2 and 2.5.
<result>E</result>
The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between
Bunuel, can you please explain this one?