Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] than the others, let's solve each equation step-by-step and compare their solutions:
1. Equation 1:
[tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To isolate [tex]\( x \)[/tex], subtract [tex]\( 11.3 \)[/tex] from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
[tex]\( -3 = -0.6x \)[/tex]
Now, 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 [tex]\( 8.3 \)[/tex] from both sides to isolate terms with [tex]\( x \)[/tex]:
[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]\( 11.3 - 0.5x = 8.3 \)[/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides to get:
[tex]\( 11.3 - 8.3 = 0.5x \)[/tex]
[tex]\( 3 = 0.5x \)[/tex]
Divide by [tex]\( 0.5 \)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{0.5} = 6 \][/tex]
4. Equation 4:
[tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
First, subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\( -0.6x = 11.3 - 8.3 \)[/tex]
[tex]\( -0.6x = 3 \)[/tex]
Divide by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{-0.6} = -5 \][/tex]
Now, compare the solutions:
- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = 5 \)[/tex]
- Equation 3: [tex]\( x = 6 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]
The equation that results in a different value of [tex]\( x \)[/tex] is Equation 3, where [tex]\( x = 6 \)[/tex].
1. Equation 1:
[tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
To isolate [tex]\( x \)[/tex], subtract [tex]\( 11.3 \)[/tex] from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
[tex]\( -3 = -0.6x \)[/tex]
Now, 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 [tex]\( 8.3 \)[/tex] from both sides to isolate terms with [tex]\( x \)[/tex]:
[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]\( 11.3 - 0.5x = 8.3 \)[/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides to get:
[tex]\( 11.3 - 8.3 = 0.5x \)[/tex]
[tex]\( 3 = 0.5x \)[/tex]
Divide by [tex]\( 0.5 \)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{0.5} = 6 \][/tex]
4. Equation 4:
[tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
First, subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\( -0.6x = 11.3 - 8.3 \)[/tex]
[tex]\( -0.6x = 3 \)[/tex]
Divide by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{-0.6} = -5 \][/tex]
Now, compare the solutions:
- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = 5 \)[/tex]
- Equation 3: [tex]\( x = 6 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]
The equation that results in a different value of [tex]\( x \)[/tex] is Equation 3, where [tex]\( x = 6 \)[/tex].
