Question

graph the functions $f(x) = -2x - 6$ and $g(x) = -2^x - 6$ on the same coordinate plane. what are the solutions of the equation $-2x - 6 = -2^x - 6$? select each correct answer. $x = -1$ $x = 0$ $x = 1$ $x = 2$ $x = 3$

Explanation:

Step1: Simplify the given equation

Start with the original equation:
$$-2x - 6 = -2^x - 6$$
Add 6 to both sides to simplify:
$$-2x = -2^x$$
Multiply both sides by -1:
$$2x = 2^x$$

Step2: Test each candidate x-value

For $x=1$:

Left side: $2(1)=2$
Right side: $2^1=2$
Both sides are equal, so $x=1$ is a solution.

For $x=2$:

Left side: $2(2)=4$
Right side: $2^2=4$
Both sides are equal, so $x=2$ is a solution.

For $x=-1$:

Left side: $2(-1)=-2$
Right side: $2^{-1}=\frac{1}{2}$
Sides are not equal, so not a solution.

For $x=0$:

Left side: $2(0)=0$
Right side: $2^0=1$
Sides are not equal, so not a solution.

For $x=3$:

Left side: $2(3)=6$
Right side: $2^3=8$
Sides are not equal, so not a solution.

Answer:

$\boldsymbol{x=1}$, $\boldsymbol{x=2}$