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Answer :
To find out which equation results in a different value of [tex]\( x \)[/tex], let's solve each equation one by one and see which one stands out.
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], first subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3.0 = -0.6x
\][/tex]
Next, divide each side by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Start by subtracting 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
Divide each side by 0.6:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Begin by subtracting 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
Divide each side by 0.6:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/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]\[
-0.6x = 3.0
\][/tex]
Divide each side by -0.6:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0
\][/tex]
By comparing the solutions, we can see that Equations 1, 2, and 3 all result in [tex]\( x = 5.0 \)[/tex]. However, Equation 4 results in [tex]\( x = -5.0 \)[/tex]. Therefore, the equation that gives a different solution is the fourth one: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], first subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3.0 = -0.6x
\][/tex]
Next, divide each side by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Start by subtracting 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
Divide each side by 0.6:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Begin by subtracting 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
Divide each side by 0.6:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/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]\[
-0.6x = 3.0
\][/tex]
Divide each side by -0.6:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0
\][/tex]
By comparing the solutions, we can see that Equations 1, 2, and 3 all result in [tex]\( x = 5.0 \)[/tex]. However, Equation 4 results in [tex]\( x = -5.0 \)[/tex]. Therefore, the equation that gives a different solution is the fourth one: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
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