Answer :
Let's solve each equation step by step to find which one results in a different value of [tex]\( x \)[/tex].
1. Equation 1:
[tex]\( 8.3 = -0.8x + 11.3 \)[/tex]
First, isolate the term containing [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = -0.8x
\][/tex]
[tex]\[
-3 = -0.8x
\][/tex]
Now, divide both sides by [tex]\(-0.8\)[/tex]:
[tex]\[
x = \frac{-3}{-0.8} = 3.75
\][/tex]
2. Equation 2:
[tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Isolate the term with [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3:
[tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Isolate the [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4:
[tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Isolate the [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]
[tex]\[
-3 = 0.6x
\][/tex]
Divide both sides by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{-3}{0.6} = -5
\][/tex]
### Conclusion:
- Equation 1 gives [tex]\( x = 3.75 \)[/tex].
- Equations 2 and 3 both give [tex]\( x = 5 \)[/tex].
- Equation 4 gives [tex]\( x = -5 \)[/tex].
Thus, the equation that results in a different value of [tex]\( x \)[/tex] from the others is Equation 1: [tex]\( 8.3 = -0.8x + 11.3 \)[/tex], which gives [tex]\( x = 3.75 \)[/tex].
1. Equation 1:
[tex]\( 8.3 = -0.8x + 11.3 \)[/tex]
First, isolate the term containing [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = -0.8x
\][/tex]
[tex]\[
-3 = -0.8x
\][/tex]
Now, divide both sides by [tex]\(-0.8\)[/tex]:
[tex]\[
x = \frac{-3}{-0.8} = 3.75
\][/tex]
2. Equation 2:
[tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Isolate the term with [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3:
[tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Isolate the [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4:
[tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Isolate the [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]
[tex]\[
-3 = 0.6x
\][/tex]
Divide both sides by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{-3}{0.6} = -5
\][/tex]
### Conclusion:
- Equation 1 gives [tex]\( x = 3.75 \)[/tex].
- Equations 2 and 3 both give [tex]\( x = 5 \)[/tex].
- Equation 4 gives [tex]\( x = -5 \)[/tex].
Thus, the equation that results in a different value of [tex]\( x \)[/tex] from the others is Equation 1: [tex]\( 8.3 = -0.8x + 11.3 \)[/tex], which gives [tex]\( x = 3.75 \)[/tex].
