Using a table of value determine the solution to the equation below to the nearest fourth of a unit

2^ (-x) + 1 = 5^x + 2

x = - 1.50

x = 2.50

x = - 0.50

x = 0.75

For finding the solution to something like this, it makes sense to write a function of x that is zero at the solution value. That function might be obtained by subtracting the right side from the equation.

f (x) = (2^-x + 1) - (5^x + 2)

Now, we want to find x so that f (x) = 0.

For the offered choices, we get

f (-1.50) ≈ 1.74

f (-0.50) ≈ - 0.03

f (0.75) ≈ - 3.75

f (2.50) ≈ - 56.72

The obvious choice is

x = - 0.50