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Answer :
To solve this problem, we need to identify which equation results in a different value for [tex]\( x \)[/tex] than the others.
Let's examine each equation and solve for [tex]\( x \)[/tex] step by step:
Equation 1:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
2. Simplify:
[tex]\[ -3.0 = -0.6x \][/tex]
3. Divide by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3.0}{-0.6} = 5.0 \][/tex]
Equation 2:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 3.0 = 0.6x \][/tex]
3. Divide by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3.0}{0.6} = 5.0 \][/tex]
Equation 3:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = -3.0 \][/tex]
3. Divide by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3.0}{-0.6} = 5.0 \][/tex]
Equation 4:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = 3.0 \][/tex]
3. Divide by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3.0}{-0.6} = -5.0 \][/tex]
After completing the calculations, we find that:
- Equations 1, 2, and 3 all give [tex]\( x = 5.0 \)[/tex].
- Equation 4 gives a different result: [tex]\( x = -5.0 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] than the other three is [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
Let's examine each equation and solve for [tex]\( x \)[/tex] step by step:
Equation 1:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
2. Simplify:
[tex]\[ -3.0 = -0.6x \][/tex]
3. Divide by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3.0}{-0.6} = 5.0 \][/tex]
Equation 2:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 3.0 = 0.6x \][/tex]
3. Divide by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3.0}{0.6} = 5.0 \][/tex]
Equation 3:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = -3.0 \][/tex]
3. Divide by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3.0}{-0.6} = 5.0 \][/tex]
Equation 4:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = 3.0 \][/tex]
3. Divide by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3.0}{-0.6} = -5.0 \][/tex]
After completing the calculations, we find that:
- Equations 1, 2, and 3 all give [tex]\( x = 5.0 \)[/tex].
- Equation 4 gives a different result: [tex]\( x = -5.0 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] than the other three is [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
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