Brianna solved a two-step equation, but she made a mistake along the way.
$\begin{aligned}
0.1 x+3 & =1.7 \\
(-3)+0.1 x+3 & =1.7+(-3) \\
0.1 x & =-1.3 \quad \text { Line } 1 \\
(-0.1)+0.1 x & =-1.3+(-0.1) \text { Line } 2 \\
x & =-1.4 \quad \text { Line } 4
\end{aligned}$
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 (1)
Brianna correctly subtracted 3 from both sides of the equation.
To isolate x, she needed to divide both sides by 0.1.
Instead, she subtracted 0.1 from both sides, which was the mistake.
Therefore, on Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1. On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1.
Explanation
Analyzing the Problem Let's analyze Brianna's steps to identify the mistake in solving the equation.
The original equation is: 0.1 x + 3 = 1.7
Brianna's steps are:
( − 3 ) + 0.1 x + 3 = 1.7 + ( − 3 )
0.1 x = − 1.3 (Line 1)
( − 0.1 ) + 0.1 x = − 1.3 + ( − 0.1 ) (Line 2)
x = − 1.4 (Line 4)
Checking Line 1 The first step Brianna took, subtracting 3 from both sides, is correct. This isolates the term with x :
0.1 x + 3 − 3 = 1.7 − 3 0.1 x = − 1.3
So, Line 1 is correct.
Identifying the Mistake To solve for x , we need to isolate x by dividing both sides of the equation 0.1 x = − 1.3 by 0.1 :
0.1 0.1 x = 0.1 − 1.3 x = − 13
However, Brianna subtracted 0.1 from both sides instead of dividing by 0.1 . This is the mistake.
Conclusion Brianna's mistake was on Line 3. She should have divided by 0.1 instead of subtracting 0.1. Subtracting 0.1 from both sides is not a valid step to isolate x .
Examples
When solving equations in physics or engineering, it's crucial to isolate the variable you're trying to find. For instance, if you're calculating the force acting on an object using the equation F = ma , and you know the mass ( m ) and acceleration ( a ), you need to isolate F to find its value. Similarly, in circuit analysis, you might need to solve for the current ( I ) in a circuit using Ohm's law, V = I R , where V is the voltage and R is the resistance. Isolating I involves dividing both sides of the equation by R . These examples show how correctly applying algebraic operations is essential for accurate problem-solving in various fields.
