Answer :
To determine which equation results in a different value for [tex]\( x \)[/tex] than the others, we need to solve each equation for [tex]\( x \)[/tex] and compare the solutions. Let's go through each equation step-by-step:
1. Equation 1:
[tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Step 1: Subtract 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
[tex]\( -3 = -0.6x \)[/tex]
- Step 2: Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{-3}{-0.6} \)[/tex]
[tex]\( x = 5 \)[/tex]
2. Equation 2:
[tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Step 1: Subtract 8.3 from both sides:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
[tex]\( 3 = 0.6x \)[/tex]
- Step 2: Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{3}{0.6} \)[/tex]
[tex]\( x = 5 \)[/tex]
3. Equation 3:
[tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Step 1: Subtract 8.3 from both sides:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
[tex]\( 3 = 0.6x \)[/tex]
- Step 2: Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{3}{0.6} \)[/tex]
[tex]\( x = 5 \)[/tex]
4. Equation 4:
[tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Step 1: Subtract 8.3 from both sides:
[tex]\( 8.3 - 11.3 = 0.6x \)[/tex]
[tex]\( -3 = 0.6x \)[/tex]
- Step 2: Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{-3}{0.6} \)[/tex]
[tex]\( x = -5 \)[/tex]
Now that we have solved all four equations:
- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = 5 \)[/tex]
- Equation 3: [tex]\( x = 5 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]
The solution for Equation 4 is different from the solutions for the other three equations. Therefore, Equation 4 results in a different value for [tex]\( x \)[/tex] than the others.
1. Equation 1:
[tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Step 1: Subtract 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
[tex]\( -3 = -0.6x \)[/tex]
- Step 2: Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{-3}{-0.6} \)[/tex]
[tex]\( x = 5 \)[/tex]
2. Equation 2:
[tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Step 1: Subtract 8.3 from both sides:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
[tex]\( 3 = 0.6x \)[/tex]
- Step 2: Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{3}{0.6} \)[/tex]
[tex]\( x = 5 \)[/tex]
3. Equation 3:
[tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Step 1: Subtract 8.3 from both sides:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
[tex]\( 3 = 0.6x \)[/tex]
- Step 2: Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{3}{0.6} \)[/tex]
[tex]\( x = 5 \)[/tex]
4. Equation 4:
[tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Step 1: Subtract 8.3 from both sides:
[tex]\( 8.3 - 11.3 = 0.6x \)[/tex]
[tex]\( -3 = 0.6x \)[/tex]
- Step 2: Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{-3}{0.6} \)[/tex]
[tex]\( x = -5 \)[/tex]
Now that we have solved all four equations:
- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = 5 \)[/tex]
- Equation 3: [tex]\( x = 5 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]
The solution for Equation 4 is different from the solutions for the other three equations. Therefore, Equation 4 results in a different value for [tex]\( x \)[/tex] than the others.
