Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the others, let's solve each one step by step:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
- Simplify:
[tex]\( -3 = -0.6x \)[/tex]
- Divide both sides by -0.6:
[tex]\( x = \frac{-3}{-0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 \)[/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]
- Simplify:
[tex]\( 3 = 0.6x \)[/tex]
- Divide both sides by 0.6:
[tex]\( x = \frac{3}{0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 \)[/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
- Simplify:
[tex]\( 3 = 0.6x \)[/tex]
- Divide both sides by 0.6:
[tex]\( x = \frac{3}{0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 \)[/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]
- Simplify:
[tex]\( -0.6x = 3 \)[/tex]
- Divide both sides by -0.6:
[tex]\( x = \frac{3}{-0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = -5 \)[/tex]
The equations that have the same solution for [tex]\( x = 5 \)[/tex] are the first three equations. The equation that results in a different value of [tex]\( x \)[/tex] is the fourth equation, which gives [tex]\( x = -5 \)[/tex]. Therefore, the fourth equation, [tex]\( 8.3 - 0.6x = 11.3 \)[/tex], is the one with a different solution.
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
- Simplify:
[tex]\( -3 = -0.6x \)[/tex]
- Divide both sides by -0.6:
[tex]\( x = \frac{-3}{-0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 \)[/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]
- Simplify:
[tex]\( 3 = 0.6x \)[/tex]
- Divide both sides by 0.6:
[tex]\( x = \frac{3}{0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 \)[/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
- Simplify:
[tex]\( 3 = 0.6x \)[/tex]
- Divide both sides by 0.6:
[tex]\( x = \frac{3}{0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 \)[/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]
- Simplify:
[tex]\( -0.6x = 3 \)[/tex]
- Divide both sides by -0.6:
[tex]\( x = \frac{3}{-0.6} \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\( x = -5 \)[/tex]
The equations that have the same solution for [tex]\( x = 5 \)[/tex] are the first three equations. The equation that results in a different value of [tex]\( x \)[/tex] is the fourth equation, which gives [tex]\( x = -5 \)[/tex]. Therefore, the fourth equation, [tex]\( 8.3 - 0.6x = 11.3 \)[/tex], is the one with a different solution.
