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Answer :
To determine the correct equation to find the value of [tex]\( x \)[/tex] when the shortest side, [tex]\( y \)[/tex], measures 2.1 meters, we need to analyze each equation option given:
1. Equation 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
2. Equation 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
3. Equation 3: [tex]\( v^{-4.2} = 7.5 \)[/tex]
4. Equation 4: [tex]\( 2.1 + 2x = 7.5 \)[/tex]
We know from the problem statement that [tex]\( y = 2.1 \)[/tex]. Let's consider each equation:
Equation 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
This equation does not directly incorporate the given information that [tex]\( y = 2.1 \)[/tex] in a helpful manner because it subtracts 2.1, which is not related to [tex]\( y \)[/tex] in a way that solves for [tex]\( x \)[/tex].
Equation 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
This equation incorporates [tex]\( y \)[/tex], but when simplified, it does not involve [tex]\( x \)[/tex] at all, so it's not relevant to finding the value of [tex]\( x \)[/tex].
Equation 3: [tex]\( v^{-4.2} = 7.5 \)[/tex]
This equation does not relate to [tex]\( x \)[/tex] and involves a different variable [tex]\( v \)[/tex], making it irrelevant to our task.
Equation 4: [tex]\( 2.1 + 2x = 7.5 \)[/tex]
This equation uses [tex]\( y = 2.1 \)[/tex] directly as a number added to [tex]\( 2x \)[/tex]. We can solve for [tex]\( x \)[/tex] from this equation:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
To isolate [tex]\( 2x \)[/tex], subtract 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
Calculate the subtraction:
[tex]\[
2x = 5.4
\][/tex]
Now, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the fourth equation, [tex]\( 2.1 + 2x = 7.5 \)[/tex], is the correct one to find the value of [tex]\( x \)[/tex] when the shortest side [tex]\( y \)[/tex] measures 2.1 m.
1. Equation 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
2. Equation 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
3. Equation 3: [tex]\( v^{-4.2} = 7.5 \)[/tex]
4. Equation 4: [tex]\( 2.1 + 2x = 7.5 \)[/tex]
We know from the problem statement that [tex]\( y = 2.1 \)[/tex]. Let's consider each equation:
Equation 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
This equation does not directly incorporate the given information that [tex]\( y = 2.1 \)[/tex] in a helpful manner because it subtracts 2.1, which is not related to [tex]\( y \)[/tex] in a way that solves for [tex]\( x \)[/tex].
Equation 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
This equation incorporates [tex]\( y \)[/tex], but when simplified, it does not involve [tex]\( x \)[/tex] at all, so it's not relevant to finding the value of [tex]\( x \)[/tex].
Equation 3: [tex]\( v^{-4.2} = 7.5 \)[/tex]
This equation does not relate to [tex]\( x \)[/tex] and involves a different variable [tex]\( v \)[/tex], making it irrelevant to our task.
Equation 4: [tex]\( 2.1 + 2x = 7.5 \)[/tex]
This equation uses [tex]\( y = 2.1 \)[/tex] directly as a number added to [tex]\( 2x \)[/tex]. We can solve for [tex]\( x \)[/tex] from this equation:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
To isolate [tex]\( 2x \)[/tex], subtract 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
Calculate the subtraction:
[tex]\[
2x = 5.4
\][/tex]
Now, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the fourth equation, [tex]\( 2.1 + 2x = 7.5 \)[/tex], is the correct one to find the value of [tex]\( x \)[/tex] when the shortest side [tex]\( y \)[/tex] measures 2.1 m.
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