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Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the others, let's take a closer look at each equation.
1. Equation 1: [tex]\( 8.3 = -17.6x + 11.3 \)[/tex]
- Rearrange this equation to solve for [tex]\( x \)[/tex]:
- Subtract 11.3 from both sides: [tex]\( 8.3 - 11.3 = -17.6x \)[/tex]
- Simplify: [tex]\( -3 = -17.6x \)[/tex]
- Divide both sides by -17.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3}{-17.6} \approx 0.170
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Rearrange the equation to solve for [tex]\( x \)[/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 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Rearrange the equation to solve for [tex]\( x \)[/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 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Rearrange this equation to solve for [tex]\( x \)[/tex]:
- Add 0.6x to both sides: [tex]\( 8.3 = 11.3 + 0.6x \)[/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 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3}{0.6} = -5
\][/tex]
Now, let's compare the solutions:
- Equation 1 gives [tex]\( x \approx 0.170 \)[/tex].
- Equation 2 gives [tex]\( x = 5 \)[/tex].
- Equation 3 gives [tex]\( x = 5 \)[/tex].
- Equation 4 gives [tex]\( x = -5 \)[/tex].
The equation that results in a different value of [tex]\( x \)[/tex] than the others is Equation 1, as its solution ([tex]\( x \approx 0.170 \)[/tex]) does not match the solution of the other three equations.
1. Equation 1: [tex]\( 8.3 = -17.6x + 11.3 \)[/tex]
- Rearrange this equation to solve for [tex]\( x \)[/tex]:
- Subtract 11.3 from both sides: [tex]\( 8.3 - 11.3 = -17.6x \)[/tex]
- Simplify: [tex]\( -3 = -17.6x \)[/tex]
- Divide both sides by -17.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3}{-17.6} \approx 0.170
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Rearrange the equation to solve for [tex]\( x \)[/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 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Rearrange the equation to solve for [tex]\( x \)[/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 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Rearrange this equation to solve for [tex]\( x \)[/tex]:
- Add 0.6x to both sides: [tex]\( 8.3 = 11.3 + 0.6x \)[/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 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3}{0.6} = -5
\][/tex]
Now, let's compare the solutions:
- Equation 1 gives [tex]\( x \approx 0.170 \)[/tex].
- Equation 2 gives [tex]\( x = 5 \)[/tex].
- Equation 3 gives [tex]\( x = 5 \)[/tex].
- Equation 4 gives [tex]\( x = -5 \)[/tex].
The equation that results in a different value of [tex]\( x \)[/tex] than the others is Equation 1, as its solution ([tex]\( x \approx 0.170 \)[/tex]) does not match the solution of the other three equations.
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