Answer :
To determine which equation, when solved, results in a different value of [tex]\( x \)[/tex] than the others, let's take a look at each equation and solve for [tex]\( x \)[/tex]:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex]:
- Subtract 11.3 from both sides:
[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]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
To solve for [tex]\( x \)[/tex]:
- Subtract 8.3 from both sides:
[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]
To solve for [tex]\( x \)[/tex]:
- Subtract 8.3 from both sides:
[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]
To solve for [tex]\( x \)[/tex]:
- Subtract 11.3 from both sides:
[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]
Comparing the results, we can see that:
- Equation 1, 2, and 3 all result in [tex]\( x = 5 \)[/tex].
- Equation 4 results in [tex]\( x = -5 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] than the others is Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex], since it gives [tex]\( x = -5 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex]:
- Subtract 11.3 from both sides:
[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]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
To solve for [tex]\( x \)[/tex]:
- Subtract 8.3 from both sides:
[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]
To solve for [tex]\( x \)[/tex]:
- Subtract 8.3 from both sides:
[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]
To solve for [tex]\( x \)[/tex]:
- Subtract 11.3 from both sides:
[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]
Comparing the results, we can see that:
- Equation 1, 2, and 3 all result in [tex]\( x = 5 \)[/tex].
- Equation 4 results in [tex]\( x = -5 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] than the others is Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex], since it gives [tex]\( x = -5 \)[/tex].
