Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the others, we need to solve each equation and find the value of [tex]\( x \)[/tex].
Let's look at each equation one by one:
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 the left side:
[tex]\[
-3.0 = -0.6x
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- First, subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
- Simplify the left side:
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6:
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Start by subtracting 8.3 from both sides:
[tex]\[
11.3 - 8.3 - 0.6x = 0
\][/tex]
- Simplify:
[tex]\[
3.0 - 0.6x = 0
\][/tex]
- Add 0.6x to both sides:
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide by 0.6:
[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:
[tex]\[
-0.6x = 3.0
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = -5
\][/tex]
After solving all the equations, we see that the first three equations give the same value of [tex]\( x = 5 \)[/tex], while the fourth equation gives a different value of [tex]\( x = -5 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] is:
Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Let's look at each equation one by one:
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 the left side:
[tex]\[
-3.0 = -0.6x
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- First, subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
- Simplify the left side:
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6:
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Start by subtracting 8.3 from both sides:
[tex]\[
11.3 - 8.3 - 0.6x = 0
\][/tex]
- Simplify:
[tex]\[
3.0 - 0.6x = 0
\][/tex]
- Add 0.6x to both sides:
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide by 0.6:
[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:
[tex]\[
-0.6x = 3.0
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = -5
\][/tex]
After solving all the equations, we see that the first three equations give the same value of [tex]\( x = 5 \)[/tex], while the fourth equation gives a different value of [tex]\( x = -5 \)[/tex].
Therefore, the equation that results in a different value of [tex]\( x \)[/tex] is:
Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
