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Answer :
We need to solve each equation for [tex]\( x \)[/tex] and compare the results.
Step 1. Solve Equation 1:
The equation is
[tex]\[
8.3 = -0.6x + 11.3.
\][/tex]
Subtract [tex]\( 11.3 \)[/tex] from both sides:
[tex]\[
8.3 - 11.3 = -0.6x,
\][/tex]
which gives
[tex]\[
-3.0 = -0.6x.
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0.
\][/tex]
Step 2. Solve Equation 2:
The equation is
[tex]\[
11.3 = 8.3 + 0.6x.
\][/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
11.3 - 8.3 = 0.6x,
\][/tex]
which simplifies to
[tex]\[
3.0 = 0.6x.
\][/tex]
Divide by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0.
\][/tex]
Step 3. Solve Equation 3:
The equation is
[tex]\[
11.3 - 0.6x = 8.3.
\][/tex]
Subtract [tex]\( 11.3 \)[/tex] from both sides:
[tex]\[
-0.6x = 8.3 - 11.3,
\][/tex]
which gives
[tex]\[
-0.6x = -3.0.
\][/tex]
Divide by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0.
\][/tex]
Step 4. Solve Equation 4:
The equation is
[tex]\[
8.3 - 0.6x = 11.3.
\][/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
-0.6x = 11.3 - 8.3,
\][/tex]
which simplifies to
[tex]\[
-0.6x = 3.0.
\][/tex]
Divide by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0.
\][/tex]
Conclusion:
The first three equations yield [tex]\( x = 5.0 \)[/tex], while the fourth equation gives [tex]\( x = -5.0 \)[/tex]. Therefore, the equation
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
produces a different result.
Thus, the equation that results in a different value of [tex]\( x \)[/tex] is Equation 4.
Step 1. Solve Equation 1:
The equation is
[tex]\[
8.3 = -0.6x + 11.3.
\][/tex]
Subtract [tex]\( 11.3 \)[/tex] from both sides:
[tex]\[
8.3 - 11.3 = -0.6x,
\][/tex]
which gives
[tex]\[
-3.0 = -0.6x.
\][/tex]
Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0.
\][/tex]
Step 2. Solve Equation 2:
The equation is
[tex]\[
11.3 = 8.3 + 0.6x.
\][/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
11.3 - 8.3 = 0.6x,
\][/tex]
which simplifies to
[tex]\[
3.0 = 0.6x.
\][/tex]
Divide by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0.
\][/tex]
Step 3. Solve Equation 3:
The equation is
[tex]\[
11.3 - 0.6x = 8.3.
\][/tex]
Subtract [tex]\( 11.3 \)[/tex] from both sides:
[tex]\[
-0.6x = 8.3 - 11.3,
\][/tex]
which gives
[tex]\[
-0.6x = -3.0.
\][/tex]
Divide by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0.
\][/tex]
Step 4. Solve Equation 4:
The equation is
[tex]\[
8.3 - 0.6x = 11.3.
\][/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
-0.6x = 11.3 - 8.3,
\][/tex]
which simplifies to
[tex]\[
-0.6x = 3.0.
\][/tex]
Divide by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0.
\][/tex]
Conclusion:
The first three equations yield [tex]\( x = 5.0 \)[/tex], while the fourth equation gives [tex]\( x = -5.0 \)[/tex]. Therefore, the equation
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
produces a different result.
Thus, the equation that results in a different value of [tex]\( x \)[/tex] is Equation 4.
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