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The third side is described in relation to one of the equal sides, so let [tex]x[/tex] be the length of one of the equal sides.

Which equation models the problem?

A. [tex]x + x + (5 - 2x) = 23[/tex]
B. [tex]x + x + (2x - 5) = 23[/tex]
C. [tex]x + x + (2x + 5) = 23[/tex]
D. [tex]x + (2x - 5) + (2x - 5) = 23[/tex]

Sagot :

GinnyAnsweridn
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]
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