Question

Order the equations from least to greatest based on the number of solutions to each equation.

Answer 1

Hello,
Please, see the attached files.
Thanks.

Answer 2

In order to answer, you need to sketch the given exponential curves and straight lines and ask yourself if and when do they cross each other:

a) 2ˣ + 1 is an esponential curve with base >1 shifted up by 1;
    -3x + 6 is a straight line with negative slope, shifted up by 6;
    They cross each others only one time.

b) 3ˣ - 3 is an esponential curve with base >1 shifted down by three, thus it can be negative;
    2x - 2 is  a straight line with positive slope shifted down by 2;
    They cross each others twice.

c) -4ˣ - 1 is an esponential curve with base >1 flipped over the x axis and shifted down by 1;
   3⁻ˣ - 2 is an esponential curve with base <1 ( 3⁻ˣ = (1/3)ˣ )and shifted down by 2;
  They never cross each others.

Therefore the correct rder is:
-4ˣ - 1 = 3⁻ˣ - 2
-3x + 6 = 2ˣ + 1
3ˣ - 3 = 2x - 2