Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] compared to the others, we need to analyze each equation separately.
1. Equation 1: [tex]\( 8.3 = -17.6x + 11.3 \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = -17.6x
\][/tex]
[tex]\[
-3.0 = -17.6x
\][/tex]
[tex]\[
x = \frac{-3.0}{-17.6} \approx 0.1705
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 17.6x \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 17.6x
\][/tex]
[tex]\[
3.0 = 17.6x
\][/tex]
[tex]\[
x = \frac{3.0}{17.6} \approx 0.1705
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]
[tex]\[
-3.0 = 0.6x
\][/tex]
[tex]\[
x = \frac{-3.0}{0.6} = -5.0
\][/tex]
After solving each equation, we have the following [tex]\( x \)[/tex] values:
- Equation 1: [tex]\( x \approx 0.1705 \)[/tex]
- Equation 2: [tex]\( x \approx 0.1705 \)[/tex]
- Equation 3: [tex]\( x = 5.0 \)[/tex]
- Equation 4: [tex]\( x = -5.0 \)[/tex]
Equations 1 and 2 result in the same value of [tex]\( x \)[/tex]. However, Equation 3 and Equation 4 give different values of [tex]\( x \)[/tex] compared to each other and to Equations 1 and 2. Therefore, Equations 3 and 4 are the ones that result in different values of [tex]\( x \)[/tex].
1. Equation 1: [tex]\( 8.3 = -17.6x + 11.3 \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = -17.6x
\][/tex]
[tex]\[
-3.0 = -17.6x
\][/tex]
[tex]\[
x = \frac{-3.0}{-17.6} \approx 0.1705
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 17.6x \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 17.6x
\][/tex]
[tex]\[
3.0 = 17.6x
\][/tex]
[tex]\[
x = \frac{3.0}{17.6} \approx 0.1705
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]
[tex]\[
-3.0 = 0.6x
\][/tex]
[tex]\[
x = \frac{-3.0}{0.6} = -5.0
\][/tex]
After solving each equation, we have the following [tex]\( x \)[/tex] values:
- Equation 1: [tex]\( x \approx 0.1705 \)[/tex]
- Equation 2: [tex]\( x \approx 0.1705 \)[/tex]
- Equation 3: [tex]\( x = 5.0 \)[/tex]
- Equation 4: [tex]\( x = -5.0 \)[/tex]
Equations 1 and 2 result in the same value of [tex]\( x \)[/tex]. However, Equation 3 and Equation 4 give different values of [tex]\( x \)[/tex] compared to each other and to Equations 1 and 2. Therefore, Equations 3 and 4 are the ones that result in different values of [tex]\( x \)[/tex].
