Answer :
To solve this problem, we need to determine which equation results in a different value for [tex]\( x \)[/tex] than the others.
Let's examine each equation one by one:
1. Equation 1: [tex]\(8.3 = -0.6x + 11.3\)[/tex]
- First, subtract 11.3 from both sides:
[tex]\(8.3 - 11.3 = -0.6x\)[/tex]
[tex]\(-3 = -0.6x\)[/tex].
- Next, divide by -0.6:
[tex]\(x = \frac{-3}{-0.6} = 5\)[/tex].
2. Equation 2: [tex]\(11.3 = 8.3 + 0.6x\)[/tex]
- Subtract 8.3 from both sides:
[tex]\(11.3 - 8.3 = 0.6x\)[/tex]
[tex]\(3 = 0.6x\)[/tex].
- Divide by 0.6:
[tex]\(x = \frac{3}{0.6} = 5\)[/tex].
3. Equation 3: [tex]\(11.3 - 0.6x = 8.3\)[/tex]
- Subtract 11.3 from both sides:
[tex]\(-0.6x = 8.3 - 11.3\)[/tex]
[tex]\(-0.6x = -3\)[/tex].
- Divide by -0.6:
[tex]\(x = \frac{-3}{-0.6} = 5\)[/tex].
4. Equation 4: [tex]\(8.3 - 0.6x = 11.3\)[/tex]
- Subtract 8.3 from both sides:
[tex]\(-0.6x = 11.3 - 8.3\)[/tex]
[tex]\(-0.6x = 3\)[/tex].
- Divide by -0.6:
[tex]\(x = \frac{3}{-0.6} = -5\)[/tex].
After solving all equations, we see that Equations 1, 2, and 3 give [tex]\( x = 5 \)[/tex], while Equation 4 gives [tex]\( x = -5 \)[/tex]. Therefore, Equation 4 results in a different value for [tex]\( x \)[/tex] than the other three equations.
Let's examine each equation one by one:
1. Equation 1: [tex]\(8.3 = -0.6x + 11.3\)[/tex]
- First, subtract 11.3 from both sides:
[tex]\(8.3 - 11.3 = -0.6x\)[/tex]
[tex]\(-3 = -0.6x\)[/tex].
- Next, divide by -0.6:
[tex]\(x = \frac{-3}{-0.6} = 5\)[/tex].
2. Equation 2: [tex]\(11.3 = 8.3 + 0.6x\)[/tex]
- Subtract 8.3 from both sides:
[tex]\(11.3 - 8.3 = 0.6x\)[/tex]
[tex]\(3 = 0.6x\)[/tex].
- Divide by 0.6:
[tex]\(x = \frac{3}{0.6} = 5\)[/tex].
3. Equation 3: [tex]\(11.3 - 0.6x = 8.3\)[/tex]
- Subtract 11.3 from both sides:
[tex]\(-0.6x = 8.3 - 11.3\)[/tex]
[tex]\(-0.6x = -3\)[/tex].
- Divide by -0.6:
[tex]\(x = \frac{-3}{-0.6} = 5\)[/tex].
4. Equation 4: [tex]\(8.3 - 0.6x = 11.3\)[/tex]
- Subtract 8.3 from both sides:
[tex]\(-0.6x = 11.3 - 8.3\)[/tex]
[tex]\(-0.6x = 3\)[/tex].
- Divide by -0.6:
[tex]\(x = \frac{3}{-0.6} = -5\)[/tex].
After solving all equations, we see that Equations 1, 2, and 3 give [tex]\( x = 5 \)[/tex], while Equation 4 gives [tex]\( x = -5 \)[/tex]. Therefore, Equation 4 results in a different value for [tex]\( x \)[/tex] than the other three equations.
