Answer :
We want to find the value of [tex]$x$[/tex] in each equation and then determine which one gives a different result.
--------------------------------------------------
1. For equation A,
[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 simplifies to:
[tex]$$
-3.0 = -0.6x.
$$[/tex]
Now, divide both sides by [tex]$-0.6$[/tex]:
[tex]$$
x = \frac{-3.0}{-0.6} = 5.0.
$$[/tex]
--------------------------------------------------
2. For equation B,
[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 gives:
[tex]$$
3.0 = 0.6x.
$$[/tex]
Now, divide both sides by [tex]$0.6$[/tex]:
[tex]$$
x = \frac{3.0}{0.6} = 5.0.
$$[/tex]
--------------------------------------------------
3. For equation C,
[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 simplifies to:
[tex]$$
-0.6x = -3.0.
$$[/tex]
Then, divide both sides by [tex]$-0.6$[/tex]:
[tex]$$
x = \frac{-3.0}{-0.6} = 5.0.
$$[/tex]
--------------------------------------------------
4. For equation D,
[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 gives:
[tex]$$
-0.6x = 3.0.
$$[/tex]
Finally, divide both sides by [tex]$-0.6$[/tex]:
[tex]$$
x = \frac{3.0}{-0.6} = -5.0.
$$[/tex]
--------------------------------------------------
Since equations A, B, and C all yield [tex]$x = 5.0$[/tex], but equation D gives [tex]$x = -5.0$[/tex], the equation that results in a different value of [tex]$x$[/tex] is:
[tex]$$\boxed{8.3-0.6x=11.3}.$$[/tex]
Thus, the answer is D.
--------------------------------------------------
1. For equation A,
[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 simplifies to:
[tex]$$
-3.0 = -0.6x.
$$[/tex]
Now, divide both sides by [tex]$-0.6$[/tex]:
[tex]$$
x = \frac{-3.0}{-0.6} = 5.0.
$$[/tex]
--------------------------------------------------
2. For equation B,
[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 gives:
[tex]$$
3.0 = 0.6x.
$$[/tex]
Now, divide both sides by [tex]$0.6$[/tex]:
[tex]$$
x = \frac{3.0}{0.6} = 5.0.
$$[/tex]
--------------------------------------------------
3. For equation C,
[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 simplifies to:
[tex]$$
-0.6x = -3.0.
$$[/tex]
Then, divide both sides by [tex]$-0.6$[/tex]:
[tex]$$
x = \frac{-3.0}{-0.6} = 5.0.
$$[/tex]
--------------------------------------------------
4. For equation D,
[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 gives:
[tex]$$
-0.6x = 3.0.
$$[/tex]
Finally, divide both sides by [tex]$-0.6$[/tex]:
[tex]$$
x = \frac{3.0}{-0.6} = -5.0.
$$[/tex]
--------------------------------------------------
Since equations A, B, and C all yield [tex]$x = 5.0$[/tex], but equation D gives [tex]$x = -5.0$[/tex], the equation that results in a different value of [tex]$x$[/tex] is:
[tex]$$\boxed{8.3-0.6x=11.3}.$$[/tex]
Thus, the answer is D.
