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Answer :
To determine which equation results in a different value of [tex]\(x\)[/tex] compared to the others, let's solve each equation for [tex]\(x\)[/tex] and compare the solutions.
1. Equation 1:
[tex]\(8.3 = -0.6x + 11.3\)[/tex]
Subtract 11.3 from both sides:
[tex]\(-3 = -0.6x\)[/tex]
Divide by -0.6:
[tex]\(x = 5\)[/tex]
2. Equation 2:
[tex]\(11.3 = 8.3 + 0.6x\)[/tex]
Subtract 8.3 from both sides:
[tex]\(3 = 0.6x\)[/tex]
Divide by 0.6:
[tex]\(x = 5\)[/tex]
3. Equation 3:
[tex]\(11.3 - 0.6x = 8.3\)[/tex]
Subtract 11.3 from both sides:
[tex]\(-0.6x = -3\)[/tex]
Divide by -0.6:
[tex]\(x = 5\)[/tex]
4. Equation 4:
[tex]\(8.3 - 0.6x = 11.3\)[/tex]
Subtract 8.3 from both sides:
[tex]\(-0.6x = 3\)[/tex]
Divide by -0.6:
[tex]\(x = -5\)[/tex]
Comparing the solutions, equations 1, 2, and 3 all give the same result, [tex]\(x = 5\)[/tex], while equation 4 results in [tex]\(x = -5\)[/tex]. Therefore, the equation that results in a different value of [tex]\(x\)[/tex] is equation 4.
1. Equation 1:
[tex]\(8.3 = -0.6x + 11.3\)[/tex]
Subtract 11.3 from both sides:
[tex]\(-3 = -0.6x\)[/tex]
Divide by -0.6:
[tex]\(x = 5\)[/tex]
2. Equation 2:
[tex]\(11.3 = 8.3 + 0.6x\)[/tex]
Subtract 8.3 from both sides:
[tex]\(3 = 0.6x\)[/tex]
Divide by 0.6:
[tex]\(x = 5\)[/tex]
3. Equation 3:
[tex]\(11.3 - 0.6x = 8.3\)[/tex]
Subtract 11.3 from both sides:
[tex]\(-0.6x = -3\)[/tex]
Divide by -0.6:
[tex]\(x = 5\)[/tex]
4. Equation 4:
[tex]\(8.3 - 0.6x = 11.3\)[/tex]
Subtract 8.3 from both sides:
[tex]\(-0.6x = 3\)[/tex]
Divide by -0.6:
[tex]\(x = -5\)[/tex]
Comparing the solutions, equations 1, 2, and 3 all give the same result, [tex]\(x = 5\)[/tex], while equation 4 results in [tex]\(x = -5\)[/tex]. Therefore, the equation that results in a different value of [tex]\(x\)[/tex] is equation 4.
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