Answer :
To solve the problem and determine which equation results in a different value of [tex]\( x \)[/tex] than the others, we need to solve each equation individually and compare the solutions. Let's go through them one by one:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides to isolate the [tex]\( x \)[/tex]-term:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
- Simplify the left side:
[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]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Subtract 8.3 from both sides to isolate the [tex]\( x \)[/tex]-term:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
- Simplify the left side:
[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]
- Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
- Simplify the right side:
[tex]\[
-0.6x = -3
\][/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]
- Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
- Simplify the right side:
[tex]\[
-0.6x = 3
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving these equations, we can see that Equations 1, 2, and 3 all give the same solution, [tex]\( x = 5 \)[/tex]. However, Equation 4 gives a different solution, [tex]\( x = -5 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] is the fourth equation: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides to isolate the [tex]\( x \)[/tex]-term:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
- Simplify the left side:
[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]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Subtract 8.3 from both sides to isolate the [tex]\( x \)[/tex]-term:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
- Simplify the left side:
[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]
- Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
- Simplify the right side:
[tex]\[
-0.6x = -3
\][/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]
- Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
- Simplify the right side:
[tex]\[
-0.6x = 3
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving these equations, we can see that Equations 1, 2, and 3 all give the same solution, [tex]\( x = 5 \)[/tex]. However, Equation 4 gives a different solution, [tex]\( x = -5 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] is the fourth equation: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
