Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] from the others, let's solve each equation step by step:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3 = -0.6x
\][/tex]
- Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/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]
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\[
8.3 - 8.3 - 0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3
\][/tex]
- Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving these equations, we can see that:
- Equations 1, 2, and 3 all yield [tex]\( x = 5 \)[/tex].
- Equation 4 yields [tex]\( x = -5 \)[/tex].
Thus, the equation that results in a different value for [tex]\( x \)[/tex] is Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3 = -0.6x
\][/tex]
- Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/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]
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by [tex]\(0.6\)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\[
8.3 - 8.3 - 0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3
\][/tex]
- Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving these equations, we can see that:
- Equations 1, 2, and 3 all yield [tex]\( x = 5 \)[/tex].
- Equation 4 yields [tex]\( x = -5 \)[/tex].
Thus, the equation that results in a different value for [tex]\( x \)[/tex] is Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex].
