Brianna solved a two-step equation, but she made a mistake along the way.
[tex]\begin{array}{l}
0.1 x+3=1.7 \\
(-3)+0.1 x+3=1.7+(-3) \\
0.1 x=-1.3 \quad \text { Line } 1 \\
(-0.1)+0.1 x=-1.3+(-0.1) \\
x=-1.4 \quad \text { Line } 2 \\
\text { Line } 4
\end{array}[/tex]
What mistake did Brianna make?
A. On Line 1, Brianna should have subtracted 3 instead of adding -3.
B. On Line 1, Brianna violated the addition property of equality.
C. On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1.
D. On Line 3, Brianna violated the addition property of equality.
Answer (2)
Brianna correctly subtracted 3 from both sides to get 0.1 x = − 1.3 .
Brianna incorrectly subtracted 0.1 from both sides instead of dividing by 0.1.
The correct operation to isolate x is to divide both sides by 0.1, resulting in x = − 13 .
Brianna's mistake was on Line 3, where she should have divided by 0.1 instead of subtracting 0.1. On Line 3, Brianna should have divided by 0.1 instead of surfacting 0.1.
Explanation
Analyze the problem The problem is to identify the mistake Brianna made while solving the equation 0.1 x + 3 = 1.7 . We need to check each step to find the error.
Check the first step The first step is to subtract 3 from both sides of the equation: 0.1 x + 3 − 3 = 1.7 − 3 0.1 x = − 1.3 . This matches Line 1, so there is no error in the first step.
Identify the mistake The next step should be to divide both sides of the equation 0.1 x = − 1.3 by 0.1 to isolate x :
0.1 0.1 x = 0.1 − 1.3 x = − 13 . However, Brianna subtracted 0.1 from both sides instead of dividing. This is the mistake.
Conclusion Therefore, Brianna's mistake was on Line 3, where she should have divided by 0.1 instead of subtracting 0.1.
Examples
When solving equations in physics, such as calculating the velocity of an object given its acceleration and time, it's crucial to isolate the variable correctly. For example, if you have the equation v = u + a t , where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, you need to isolate a to find the acceleration. Making mistakes in algebraic manipulation can lead to incorrect results and misinterpretations of physical phenomena. Correctly applying inverse operations ensures accurate calculations and a better understanding of the relationships between physical quantities.
Brianna made a mistake on Line 3 by subtracting 0.1 instead of dividing by 0.1. The correct operation to isolate x is to perform a division. Therefore, the correct answer is On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1.
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