To solve this problem, we need to determine which equation accurately describes the scenario. Let's go through each equation step by step.
1. Equation 1: [tex]\( x + x + (5 - 2x) = 23 \)[/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 2x + (5 - 2x) = 23 \][/tex]
- Simplify inside the parentheses:
[tex]\[ 2x - 2x + 5 = 23 \][/tex]
- This reduces to:
[tex]\[ 5 = 23 \][/tex]
Since [tex]\( 5 \neq 23 \)[/tex], this equation is incorrect.
2. Equation 2: [tex]\( x + x + (2x - 5) = 23 \)[/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 2x + (2x - 5) = 23 \][/tex]
- Simplify inside the parentheses:
[tex]\[ 2x + 2x - 5 = 23 \][/tex]
- Combine like terms:
[tex]\[ 4x - 5 = 23 \][/tex]
This simplifies to the equation [tex]\( 4x - 5 = 23 \)[/tex], which is a correct and valid equation for this problem.
3. Equation 3: [tex]\( x + x + (2x + 5) = 23 \)[/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 2x + (2x + 5) = 23 \][/tex]
- Simplify inside the parentheses:
[tex]\[ 2x + 2x + 5 = 23 \][/tex]
- Combine like terms:
[tex]\[ 4x + 5 = 23 \][/tex]
This simplifies to the equation [tex]\( 4x + 5 = 23 \)[/tex], which is also a correct and valid equation for this problem.
4. Equation 4: [tex]\( x + (2x - 5) + (2x - 5) = 23 \)[/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ x + 2x - 5 + 2x - 5 = 23 \][/tex]
- Combine like terms:
[tex]\[ x + 2x + 2x - 10 = 23 \][/tex]
- Simplify:
[tex]\[ 5x - 10 = 23 \][/tex]
This simplifies to the equation [tex]\( 5x - 10 = 23 \)[/tex], which is a correct and valid equation for this problem.
Therefore, we have found three valid equations:
- [tex]\( 4x - 5 = 23 \)[/tex],
- [tex]\( 4x + 5 = 23 \)[/tex], and
- [tex]\( 5x - 10 = 23 \)[/tex].
So, the correct equations modeling the problem are:
- [tex]\( x + x + (2x - 5) = 23 \)[/tex]
- [tex]\( x + x + (2x + 5) = 23 \)[/tex]
- [tex]\( x + (2x - 5) + (2x - 5) = 23 \)[/tex]
