Answer :
Let's analyze each of the given equations step-by-step and solve for [tex]\( x \)[/tex]:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplifying the left-hand side:
[tex]\[
-3 = -0.6x
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3}{-0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
11.3 = 8.3 + 0.6x
\][/tex]
Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying the left-hand side:
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by 0.6:
[tex]\[
x = \frac{3}{0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
Subtract 11.3 from both sides and multiply by -1:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
Simplifying the left-hand side and right-hand side:
[tex]\[
-0.6x = -3
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3}{-0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
Simplifying the left-hand side and right-hand side:
[tex]\[
-0.6x = 3
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{3}{-0.6}
\][/tex]
[tex]\[
x = -5
\][/tex]
Therefore, the equations resulting in [tex]\( x = 5 \)[/tex] are the first three:
- [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
The equation resulting in [tex]\( x = -5 \)[/tex] is:
- [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Hence, the equation that results in a different value of [tex]\( x \)[/tex] than the other three is:
[tex]\[ \boxed{8.3 - 0.6 x = 11.3} \][/tex]
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplifying the left-hand side:
[tex]\[
-3 = -0.6x
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3}{-0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
11.3 = 8.3 + 0.6x
\][/tex]
Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying the left-hand side:
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by 0.6:
[tex]\[
x = \frac{3}{0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
Subtract 11.3 from both sides and multiply by -1:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
Simplifying the left-hand side and right-hand side:
[tex]\[
-0.6x = -3
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3}{-0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
Simplifying the left-hand side and right-hand side:
[tex]\[
-0.6x = 3
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{3}{-0.6}
\][/tex]
[tex]\[
x = -5
\][/tex]
Therefore, the equations resulting in [tex]\( x = 5 \)[/tex] are the first three:
- [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
The equation resulting in [tex]\( x = -5 \)[/tex] is:
- [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Hence, the equation that results in a different value of [tex]\( x \)[/tex] than the other three is:
[tex]\[ \boxed{8.3 - 0.6 x = 11.3} \][/tex]
