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Answer :
Sure! Let's solve each equation step by step to find out which one gives a different value of [tex]\( x \)[/tex] than the others.
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we'll first move 11.3 to the left side by subtracting 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplifying this gives:
[tex]\[
-3.0 = -0.6x
\][/tex]
Finally, divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2: [tex]\( 113 = 83 + 0.6x \)[/tex]
Similar to the first equation, we'll first move 83 to the left by subtracting it from both sides:
[tex]\[
113 - 83 = 0.6x
\][/tex]
Simplifying this gives:
[tex]\[
30 = 0.6x
\][/tex]
Now, divide both sides by 0.6 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{30}{0.6} = 50.0
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
We'll start by moving 11.3 to the other side by subtracting 11.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying gives:
[tex]\[
3.0 = 0.6x
\][/tex]
Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Start by moving 8.3 to the right side by subtracting 8.3 from both sides:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]
Simplifying gives:
[tex]\[
-3.0 = 0.6x
\][/tex]
Divide both sides by 0.6 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{0.6} = -5.0
\][/tex]
From the solutions above, the values of [tex]\( x \)[/tex] are [tex]\( 5.0 \)[/tex], [tex]\( 50.0 \)[/tex], [tex]\( 5.0 \)[/tex], and [tex]\( -5.0 \)[/tex]. The equation that results in a different value of [tex]\( x \)[/tex] than the other three is Equation 2, which gives [tex]\( x = 50.0 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], we'll first move 11.3 to the left side by subtracting 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplifying this gives:
[tex]\[
-3.0 = -0.6x
\][/tex]
Finally, divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0
\][/tex]
2. Equation 2: [tex]\( 113 = 83 + 0.6x \)[/tex]
Similar to the first equation, we'll first move 83 to the left by subtracting it from both sides:
[tex]\[
113 - 83 = 0.6x
\][/tex]
Simplifying this gives:
[tex]\[
30 = 0.6x
\][/tex]
Now, divide both sides by 0.6 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{30}{0.6} = 50.0
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
We'll start by moving 11.3 to the other side by subtracting 11.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying gives:
[tex]\[
3.0 = 0.6x
\][/tex]
Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Start by moving 8.3 to the right side by subtracting 8.3 from both sides:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]
Simplifying gives:
[tex]\[
-3.0 = 0.6x
\][/tex]
Divide both sides by 0.6 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{0.6} = -5.0
\][/tex]
From the solutions above, the values of [tex]\( x \)[/tex] are [tex]\( 5.0 \)[/tex], [tex]\( 50.0 \)[/tex], [tex]\( 5.0 \)[/tex], and [tex]\( -5.0 \)[/tex]. The equation that results in a different value of [tex]\( x \)[/tex] than the other three is Equation 2, which gives [tex]\( x = 50.0 \)[/tex].
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