Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the other three, let's look at each equation one by one.
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve this equation for [tex]\( x \)[/tex], we'll first move the constant term from the right side to the left by subtracting [tex]\( 11.3 \)[/tex] from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplifying the left side gives:
[tex]\[
-3 = -0.6x
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex] 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]
First, move the constant term from the right side by subtracting [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying the left side gives:
[tex]\[
3 = 0.6x
\][/tex]
Dividing both sides by [tex]\(0.6\)[/tex] 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]
Start by moving the constant [tex]\( 8.3 \)[/tex] to the left side by subtracting from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying the left side gives:
[tex]\[
3 = 0.6x
\][/tex]
Dividing both sides by [tex]\(0.6\)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Here, subtract [tex]\( 8.3 \)[/tex] from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
Simplifying the right side gives:
[tex]\[
-0.6x = 3
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
Comparing the results, we find that:
- The values of [tex]\( x \)[/tex] for Equations 1, 2, and 3 are all [tex]\( x = 5 \)[/tex].
- The value of [tex]\( x \)[/tex] for Equation 4 is [tex]\( x = -5 \)[/tex].
Thus, the equation that results in a different value of [tex]\( x \)[/tex] than the other three is Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve this equation for [tex]\( x \)[/tex], we'll first move the constant term from the right side to the left by subtracting [tex]\( 11.3 \)[/tex] from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplifying the left side gives:
[tex]\[
-3 = -0.6x
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex] 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]
First, move the constant term from the right side by subtracting [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying the left side gives:
[tex]\[
3 = 0.6x
\][/tex]
Dividing both sides by [tex]\(0.6\)[/tex] 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]
Start by moving the constant [tex]\( 8.3 \)[/tex] to the left side by subtracting from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying the left side gives:
[tex]\[
3 = 0.6x
\][/tex]
Dividing both sides by [tex]\(0.6\)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Here, subtract [tex]\( 8.3 \)[/tex] from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
Simplifying the right side gives:
[tex]\[
-0.6x = 3
\][/tex]
Dividing both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
Comparing the results, we find that:
- The values of [tex]\( x \)[/tex] for Equations 1, 2, and 3 are all [tex]\( x = 5 \)[/tex].
- The value of [tex]\( x \)[/tex] for Equation 4 is [tex]\( x = -5 \)[/tex].
Thus, the equation that results in a different value of [tex]\( x \)[/tex] than the other three is Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex].
