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

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

Exponential function

Many things that seem threatening in the dark become welcoming when we shine light on them