Answer :
Let's solve each equation to find out which one results in a different value of [tex]\( x \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we first isolate the terms involving [tex]\( x \)[/tex].
- Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3.0 = -0.6x
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Again, isolate the terms involving [tex]\( x \)[/tex].
- Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Let's solve for [tex]\( x \)[/tex].
- Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3.0
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Solve for [tex]\( x \)[/tex].
- Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3.0
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0
\][/tex]
From our calculations, equations 1, 2, and 3 all yield a solution of [tex]\( x = 5.0 \)[/tex]. Equation 4, however, results in [tex]\( x = -5.0 \)[/tex]. Therefore, the equation that results in a different value of [tex]\( x \)[/tex] 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], we first isolate the terms involving [tex]\( x \)[/tex].
- Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3.0 = -0.6x
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Again, isolate the terms involving [tex]\( x \)[/tex].
- Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
Let's solve for [tex]\( x \)[/tex].
- Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-0.6x = -3.0
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Solve for [tex]\( x \)[/tex].
- Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3.0
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{3.0}{-0.6} = -5.0
\][/tex]
From our calculations, equations 1, 2, and 3 all yield a solution of [tex]\( x = 5.0 \)[/tex]. Equation 4, however, results in [tex]\( x = -5.0 \)[/tex]. Therefore, the equation that results in a different value of [tex]\( x \)[/tex] is the fourth one: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
