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Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex], let's analyze each equation step by step:
1. Equation 1: [tex]\(8.3 = -0.6x + 11.3\)[/tex]
To solve for [tex]\( x \)[/tex], subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3 = -0.6x
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\(11.3 = 8.3 + 0.6x\)[/tex]
Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\(11.3 - 0.6x = 8.3\)[/tex]
Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = 5
\][/tex]
4. Equation 4: [tex]\(8.3 - 0.6x = 11.3\)[/tex]
Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = -5
\][/tex]
From these calculations, we see that Equations 1, 2, and 3 all result in [tex]\( x = 5 \)[/tex], while Equation 4 results in [tex]\( x = -5 \)[/tex]. Therefore, Equation 4 is the one that results in a different value of [tex]\( x \)[/tex] than the other three.
1. Equation 1: [tex]\(8.3 = -0.6x + 11.3\)[/tex]
To solve for [tex]\( x \)[/tex], subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3 = -0.6x
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\(11.3 = 8.3 + 0.6x\)[/tex]
Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\(11.3 - 0.6x = 8.3\)[/tex]
Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = 5
\][/tex]
4. Equation 4: [tex]\(8.3 - 0.6x = 11.3\)[/tex]
Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = -5
\][/tex]
From these calculations, we see that Equations 1, 2, and 3 all result in [tex]\( x = 5 \)[/tex], while Equation 4 results in [tex]\( x = -5 \)[/tex]. Therefore, Equation 4 is the one that results in a different value of [tex]\( x \)[/tex] than the other three.
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