Sure, let's solve the equation step by step:
1. Start with the given equation:
[tex]\[
2(3 - x) = 16(x + 1)
\][/tex]
2. Distribute the constants on both sides of the equation:
[tex]\[
2 \cdot 3 - 2 \cdot x = 16 \cdot x + 16 \cdot 1
\][/tex]
This simplifies to:
[tex]\[
6 - 2x = 16x + 16
\][/tex]
3. Combine like terms by getting all x terms on one side and constants on the other side. Let's move the [tex]\( -2x \)[/tex] term to the right side and the constant [tex]\( 16 \)[/tex] to the left:
[tex]\[
6 - 16 = 16x + 2x
\][/tex]
This simplifies to:
[tex]\[
-10 = 18x
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 18:
[tex]\[
x = \frac{-10}{18}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = \frac{-5}{9}
\][/tex]
So, the solution is:
[tex]\[
x = -\frac{5}{9}
\][/tex]
In decimal form, this is approximately:
[tex]\[
x \approx -0.5555555555555556
\][/tex]
