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Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the others, let's solve each one step by step:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Start by isolating [tex]\( x \)[/tex] on one side. 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 [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]
- Start by subtracting 8.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[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]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 8.3 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]
Comparing the solutions:
- For equations 1, 2, and 3, the value of [tex]\( x \)[/tex] is 5.0.
- For equation 4, the value of [tex]\( x \)[/tex] is -5.0.
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]
- Start by isolating [tex]\( x \)[/tex] on one side. 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 [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]
- Start by subtracting 8.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[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]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 8.3 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]
Comparing the solutions:
- For equations 1, 2, and 3, the value of [tex]\( x \)[/tex] is 5.0.
- For equation 4, the value of [tex]\( x \)[/tex] is -5.0.
The equation that results in a different value of [tex]\( x \)[/tex] is the fourth one: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
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