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Answer :
To find out which equation results in a different value of [tex]\( x \)[/tex] than the others, we need to carefully analyze and solve each equation provided. Let's break down the process for each one:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- First, isolate [tex]\( x \)[/tex] by subtracting 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
- This simplifies to:
[tex]\( -3.0 = -0.6x \)[/tex]
- Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{-3.0}{-0.6} \)[/tex]
- Simplifying gives:
[tex]\( x = 5 \)[/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Subtract 8.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
- Simplify to:
[tex]\( 3.0 = 0.6x \)[/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{3.0}{0.6} \)[/tex]
- This gives:
[tex]\( x = 5 \)[/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]
- Simplify the right side:
[tex]\( -0.6x = -3.0 \)[/tex]
- Divide by [tex]\(-0.6\)[/tex]:
[tex]\( x = \frac{-3.0}{-0.6} \)[/tex]
- This means:
[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 the right side:
[tex]\( -0.6x = 3.0 \)[/tex]
- Divide by [tex]\(-0.6\)[/tex]:
[tex]\( x = \frac{3.0}{-0.6} \)[/tex]
- Therefore:
[tex]\( x = -5 \)[/tex]
Upon comparing these results, we see that the value of [tex]\( x \)[/tex] for the first three equations is 5, while the last equation gives [tex]\( x = -5 \)[/tex]. Therefore, the equation [tex]\( 8.3 - 0.6x = 11.3 \)[/tex] (Equation 4) is the one that results in a different value for [tex]\( x \)[/tex] compared to the other three equations.
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- First, isolate [tex]\( x \)[/tex] by subtracting 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
- This simplifies to:
[tex]\( -3.0 = -0.6x \)[/tex]
- Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{-3.0}{-0.6} \)[/tex]
- Simplifying gives:
[tex]\( x = 5 \)[/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Subtract 8.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\( 11.3 - 8.3 = 0.6x \)[/tex]
- Simplify to:
[tex]\( 3.0 = 0.6x \)[/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\( x = \frac{3.0}{0.6} \)[/tex]
- This gives:
[tex]\( x = 5 \)[/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]
- Simplify the right side:
[tex]\( -0.6x = -3.0 \)[/tex]
- Divide by [tex]\(-0.6\)[/tex]:
[tex]\( x = \frac{-3.0}{-0.6} \)[/tex]
- This means:
[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 the right side:
[tex]\( -0.6x = 3.0 \)[/tex]
- Divide by [tex]\(-0.6\)[/tex]:
[tex]\( x = \frac{3.0}{-0.6} \)[/tex]
- Therefore:
[tex]\( x = -5 \)[/tex]
Upon comparing these results, we see that the value of [tex]\( x \)[/tex] for the first three equations is 5, while the last equation gives [tex]\( x = -5 \)[/tex]. Therefore, the equation [tex]\( 8.3 - 0.6x = 11.3 \)[/tex] (Equation 4) is the one that results in a different value for [tex]\( x \)[/tex] compared to the other three equations.
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