Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the others, we need to solve each equation separately for [tex]\( x \)[/tex] and compare the solutions.
Let's go through each equation:
1. Equation 1:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
To solve for [tex]\( x \)[/tex], first subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplify:
[tex]\[
-3.0 = -0.6x
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5
\][/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]\[
3.0 = 0.6x
\][/tex]
Divide both sides by 0.6:
[tex]\[
x = \frac{3.0}{0.6} = 5
\][/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:
[tex]\[
-0.6x = -3.0
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5
\][/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:
[tex]\[
-0.6x = 3.0
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{3.0}{-0.6} = -5
\][/tex]
After solving all the equations, we find the solutions:
- Equation 1 gives [tex]\( x = 5 \)[/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] is Equation 4.
Let's go through each equation:
1. Equation 1:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
To solve for [tex]\( x \)[/tex], first subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplify:
[tex]\[
-3.0 = -0.6x
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5
\][/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]\[
3.0 = 0.6x
\][/tex]
Divide both sides by 0.6:
[tex]\[
x = \frac{3.0}{0.6} = 5
\][/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:
[tex]\[
-0.6x = -3.0
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{-3.0}{-0.6} = 5
\][/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:
[tex]\[
-0.6x = 3.0
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{3.0}{-0.6} = -5
\][/tex]
After solving all the equations, we find the solutions:
- Equation 1 gives [tex]\( x = 5 \)[/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] is Equation 4.
