Let's analyze each equation one by one to determine which one can be used to solve for [tex]\( x \)[/tex], the amount of [tex]\( CO_2 \)[/tex] produced by the United States from transportation in 2012.
1. Equation 1: [tex]\( 2,068 \times 32 = \frac{x}{28} \)[/tex]
- By simplifying, we can calculate the left-hand side (LHS) and match it with the right-hand side (RHS).
- LHS: [tex]\( 2,068 \times 32 = 66,176 \)[/tex]
- RHS: [tex]\( \frac{x}{28} \)[/tex]
- Thus, the equation becomes [tex]\( 66,176 = \frac{x}{28} \)[/tex], which suggests [tex]\( x = 66,176 \times 28 \)[/tex] can be solved for [tex]\( x \)[/tex].
2. Equation 2: [tex]\( \frac{z}{32} = \frac{2068}{28} \)[/tex]
- By simplifying, we can see the relationship it describes.
- LHS: [tex]\( \frac{z}{32} \)[/tex]
- RHS: [tex]\( \frac{2068}{28} \)[/tex] which simplifies numerically to approximately [tex]\( 73.8571 \)[/tex]
- Simplifying the equation yields [tex]\( z \approx 73.8571 \times 32 \)[/tex] which can be evaluated to solve for [tex]\( z \)[/tex].
3. Equation 3: [tex]\( 2,068 / 32 = 2 / 28 \)[/tex]
- By simplifying, we can evaluate if the LHS equals the RHS.
- LHS: [tex]\( 2,068 / 32 \approx 64.625 \)[/tex]
- RHS: [tex]\( 2 / 28 \approx 0.0714 \)[/tex]
- Since [tex]\( 64.625 \neq 0.0714 \)[/tex], this equation is false and cannot be used to solve for [tex]\( x \)[/tex] or [tex]\( z \)[/tex].
4. Equation 4: [tex]\( \frac{32}{28} = \frac{2}{2,068} \)[/tex]
- By simplifying, we can evaluate if the LHS equals the RHS.
- LHS: [tex]\( \frac{32}{28} \approx 1.1429 \)[/tex]
- RHS: [tex]\( \frac{2}{2,068} \approx 0.000967 \)[/tex]
- Since [tex]\( 1.1429 \neq 0.000967 \)[/tex], this equation is also false and cannot be used to solve for [tex]\( x \)[/tex] or [tex]\( z \)[/tex].
Thus, the correct equation that can be used to solve for [tex]\( x \)[/tex] is:
[tex]\[ 2,068 \times 32 = \frac{x}{28} \][/tex]
Through the analysis above, we determined that this is the only true equation among the given options that allows for solving the problem [tex]\( x = 66,176 \times 28 \)[/tex] correctly representing the amount of [tex]\( CO_2 \)[/tex] produced from transportation.
