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Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] compared to the other three, let's solve each equation step by step.
1. Equation 1:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3.0
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2:
[tex]\[
11.3 = 8.3 + 0.6x
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
0.6x = 3.0
\][/tex]
Dividing both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
3. Equation 3:
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3.0
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
4. Equation 4:
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3.0
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0
\][/tex]
The values of [tex]\( x \)[/tex] for the four equations are [tex]\( 5.0 \)[/tex], [tex]\( 5.0 \)[/tex], [tex]\( 5.0 \)[/tex], and [tex]\(-5.0\)[/tex] respectively. The equation that results in a different value of [tex]\( x \)[/tex] is Equation 4.
1. Equation 1:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3.0
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2:
[tex]\[
11.3 = 8.3 + 0.6x
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
0.6x = 3.0
\][/tex]
Dividing both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
3. Equation 3:
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3.0
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
4. Equation 4:
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3.0
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0
\][/tex]
The values of [tex]\( x \)[/tex] for the four equations are [tex]\( 5.0 \)[/tex], [tex]\( 5.0 \)[/tex], [tex]\( 5.0 \)[/tex], and [tex]\(-5.0\)[/tex] respectively. The equation that results in a different value of [tex]\( x \)[/tex] is Equation 4.
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