Question

Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.

2x-4=3^-x +1

Answer 1

2x-4=3-x +1
Simplifying 2x + -4 = 3 + -1x + 1
 Reorder the terms: -4 + 2x = 3 + -1x + 1
 Reorder the terms: -4 + 2x = 3 + 1 + -1x
 Combine like terms: 3 + 1 = 4 -4 + 2x = 4 + -1x
 Solving -4 + 2x = 4 + -1x
 Solving for variable 'x'.
 Move all terms containing x to the left, all other terms to the right.
 Add 'x' to each side of the equation. -4 + 2x + x = 4 + -1x + x
 Combine like terms: 2x + x = 3x -4 + 3x = 4 + -1x + x
 Combine like terms: -1x + x = 0 -4 + 3x = 4 + 0 -4 + 3x = 4
 Add '4' to each side of the equation. -4 + 4 + 3x = 4 + 4
 Combine like terms: -4 + 4 = 0 0 + 3x = 4 + 4 3x = 4 + 4
Combine like terms: 4 + 4 = 8 3x = 8
 Divide each side by '3'. x = 2.666666667
 Simplifying x = 2.666666667

Answer 2

Answer:

The solution of the given equation is $x\approx 2.5$.

Step-by-step explanation:

The given equation is

$2x-4=3^{-x}+1$

Write the equation in system of questions.

$f(x)=2x-4$

$g(x)=3^{-x}+1$

The table of values is

x values                f(x)                   g(x)

   0                        -4                      2

   1                         -2                      1.33

   2                         0                      1.11

   3                         2                      1.037

   4                         4                      1.0123

In initial stage the value of f(x)<g(x) upto x=2. But after x=3, f(x)>g(x). It means the value of x must be lie between 2 and 3.

From the below figure it is clear that the intersection point of both functions is (2.531, 1.062).

$x=2.531$

$x\approx 2.5$

Therefore the solution of the given equation is $x\approx 2.5$.