Answer :
To determine which of the four equations results in a different value of [tex]\( x \)[/tex] than the others, we need to solve each equation for [tex]\( x \)[/tex]. Let's examine each one step-by-step:
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3.0 = -0.6x
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Subtract 8.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 8.3 from both sides to focus on terms involving [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6}
\][/tex]
[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]
[tex]\[
-0.6x = 3.0
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{-0.6}
\][/tex]
[tex]\[
x = -5
\][/tex]
Upon solving, we find that Equations 1, 2, and 3 all yield [tex]\( x = 5 \)[/tex], whereas Equation 4 yields [tex]\( x = -5 \)[/tex]. Therefore, Equation 4 results in a different value of [tex]\( x \)[/tex] than the other three equations.
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3.0 = -0.6x
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Subtract 8.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6}
\][/tex]
[tex]\[
x = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 8.3 from both sides to focus on terms involving [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3.0 = 0.6x
\][/tex]
- Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6}
\][/tex]
[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]
[tex]\[
-0.6x = 3.0
\][/tex]
- Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3.0}{-0.6}
\][/tex]
[tex]\[
x = -5
\][/tex]
Upon solving, we find that Equations 1, 2, and 3 all yield [tex]\( x = 5 \)[/tex], whereas Equation 4 yields [tex]\( x = -5 \)[/tex]. Therefore, Equation 4 results in a different value of [tex]\( x \)[/tex] than the other three equations.
