Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the others, let's go through each equation and solve them for [tex]\( x \)[/tex].
1. Equation 1: [tex]\( 8.3 = -1.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], first isolate [tex]\( x \)[/tex].
[tex]\[
8.3 = -1.6x + 11.3
\][/tex]
Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -1.6x
\][/tex]
[tex]\[
-3 = -1.6x
\][/tex]
Divide both sides by -1.6:
[tex]\[
x = \frac{-3}{-1.6} = 1.875
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Again, isolate [tex]\( x \)[/tex].
[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 0.6:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 5.6x = 8.3 \)[/tex]
Isolate [tex]\( x \)[/tex] by first rearranging the equation.
[tex]\[
11.3 - 5.6x = 8.3
\][/tex]
Subtract 11.3 from both sides:
[tex]\[
-5.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-5.6x = -3
\][/tex]
Divide both sides by -5.6:
[tex]\[
x = \frac{-3}{-5.6} \approx 0.5357
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Solve for [tex]\( x \)[/tex] by isolating it.
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving all the equations, the solutions for [tex]\( x \)[/tex] are as follows:
- Equation 1: [tex]\( x = 1.875 \)[/tex]
- Equation 2: [tex]\( x = 5.000 \)[/tex]
- Equation 3: [tex]\( x \approx 0.5357 \)[/tex]
- Equation 4: [tex]\( x = -5.000 \)[/tex]
The equation that results in a different value of [tex]\( x \)[/tex] than the others is Equation 1 which gives [tex]\( x = 1.875 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -1.6x + 11.3 \)[/tex]
To solve for [tex]\( x \)[/tex], first isolate [tex]\( x \)[/tex].
[tex]\[
8.3 = -1.6x + 11.3
\][/tex]
Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -1.6x
\][/tex]
[tex]\[
-3 = -1.6x
\][/tex]
Divide both sides by -1.6:
[tex]\[
x = \frac{-3}{-1.6} = 1.875
\][/tex]
2. Equation 2: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
Again, isolate [tex]\( x \)[/tex].
[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 0.6:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
3. Equation 3: [tex]\( 11.3 - 5.6x = 8.3 \)[/tex]
Isolate [tex]\( x \)[/tex] by first rearranging the equation.
[tex]\[
11.3 - 5.6x = 8.3
\][/tex]
Subtract 11.3 from both sides:
[tex]\[
-5.6x = 8.3 - 11.3
\][/tex]
[tex]\[
-5.6x = -3
\][/tex]
Divide both sides by -5.6:
[tex]\[
x = \frac{-3}{-5.6} \approx 0.5357
\][/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Solve for [tex]\( x \)[/tex] by isolating it.
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3
\][/tex]
Divide both sides by -0.6:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving all the equations, the solutions for [tex]\( x \)[/tex] are as follows:
- Equation 1: [tex]\( x = 1.875 \)[/tex]
- Equation 2: [tex]\( x = 5.000 \)[/tex]
- Equation 3: [tex]\( x \approx 0.5357 \)[/tex]
- Equation 4: [tex]\( x = -5.000 \)[/tex]
The equation that results in a different value of [tex]\( x \)[/tex] than the others is Equation 1 which gives [tex]\( x = 1.875 \)[/tex].
