Answer :
To determine which equation results in a different value for [tex]\( x \)[/tex] than the others, let's solve each equation individually and compare the solutions.
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]\[ -3 = -0.6x \][/tex]
3. Divide both sides by -0.6:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/tex]
Equation 2:
[tex]\[ 113 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 113 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 104.7 = 0.6x \][/tex]
3. Divide both sides by 0.6:
[tex]\[ x = \frac{104.7}{0.6} = 174.5 \][/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]\[ -0.6x = -3 \][/tex]
3. Divide both sides by -0.6:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/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]\[ -0.6x = 3 \][/tex]
3. Divide both sides by -0.6:
[tex]\[ x = \frac{3}{-0.6} = -5 \][/tex]
Now, let's look at the solutions:
- Equation 1 gives [tex]\( x = 5 \)[/tex]
- Equation 2 gives [tex]\( x = 174.5 \)[/tex]
- Equation 3 gives [tex]\( x = 5 \)[/tex]
- Equation 4 gives [tex]\( x = -5 \)[/tex]
The solutions from Equations 1, 3, and 4 are the same, but Equation 2 gives a different solution. Therefore, Equation 2 results in a different value for [tex]\( x \)[/tex] than the other three.
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]\[ -3 = -0.6x \][/tex]
3. Divide both sides by -0.6:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/tex]
Equation 2:
[tex]\[ 113 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 113 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 104.7 = 0.6x \][/tex]
3. Divide both sides by 0.6:
[tex]\[ x = \frac{104.7}{0.6} = 174.5 \][/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]\[ -0.6x = -3 \][/tex]
3. Divide both sides by -0.6:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/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]\[ -0.6x = 3 \][/tex]
3. Divide both sides by -0.6:
[tex]\[ x = \frac{3}{-0.6} = -5 \][/tex]
Now, let's look at the solutions:
- Equation 1 gives [tex]\( x = 5 \)[/tex]
- Equation 2 gives [tex]\( x = 174.5 \)[/tex]
- Equation 3 gives [tex]\( x = 5 \)[/tex]
- Equation 4 gives [tex]\( x = -5 \)[/tex]
The solutions from Equations 1, 3, and 4 are the same, but Equation 2 gives a different solution. Therefore, Equation 2 results in a different value for [tex]\( x \)[/tex] than the other three.
