Question
Eliana tried to solve 3.2+2(2.4–2t)=
–
16+t. Here is her work:
3.2+4.8–4t
=
–
16+t Step 1
8–4t
=
–
16+t Step 2
8–3t
=
–
16 Step 3
–
3t
=
–
24 Step 4
t
= 8 Step 5
Did Eliana solve the equation correctly?
which step did they mess up on what property
–
16+t. Here is her work:
3.2+4.8–4t
=
–
16+t Step 1
8–4t
=
–
16+t Step 2
8–3t
=
–
16 Step 3
–
3t
=
–
24 Step 4
t
= 8 Step 5
Did Eliana solve the equation correctly?
which step did they mess up on what property
Answers
GPT-4o mini
Let's solve the equation step by step to identify where Eliana made a mistake.
The original equation is:
\[ 3.2 + 2(2.4 - 2t) = -16 + t \]
**Step 1:** Distribute \(2\) into \((2.4 - 2t)\):
\[ 3.2 + 4.8 - 4t = -16 + t \]
Eliana did this step correctly.
**Step 2:** Combine the constants on the left side:
\[ 8 - 4t = -16 + t \]
Eliana also did this step correctly.
**Step 3:** Move the \(t\) term from the right side to the left side by adding \(4t\) to both sides and \(16\) to both sides to isolate \(t\):
\[ 8 + 16 = t + 4t \]
This gives:
\[ 24 = 5t \]
**Step 4:** Solve for \(t\):
\[ t = \frac{24}{5} = 4.8 \]
Eliana should have arrived at \(t = 4.8\), but she mistakenly combined terms in step 3.
Now, looking at Eliana's steps:
1. **Step 3 (Where she messed up):**
Eliana wrote \(8 - 3t = -16\)
instead of \(8 + 16 = 5t\). She incorrectly combined the terms involving \(t\) on the right side.
2. **Property Used/Faulted:**
She didn’t apply the property correctly for balancing the equation when isolating \(t\).
Thus, Eliana's mistake happened in the third step where she combined the terms incorrectly. The correct process would involve moving all terms involving \(t\) to one side and the constants (8 and -16) to the other side correctly. The answer should be \(t = 4.8\), not \(t = 8\).
The original equation is:
\[ 3.2 + 2(2.4 - 2t) = -16 + t \]
**Step 1:** Distribute \(2\) into \((2.4 - 2t)\):
\[ 3.2 + 4.8 - 4t = -16 + t \]
Eliana did this step correctly.
**Step 2:** Combine the constants on the left side:
\[ 8 - 4t = -16 + t \]
Eliana also did this step correctly.
**Step 3:** Move the \(t\) term from the right side to the left side by adding \(4t\) to both sides and \(16\) to both sides to isolate \(t\):
\[ 8 + 16 = t + 4t \]
This gives:
\[ 24 = 5t \]
**Step 4:** Solve for \(t\):
\[ t = \frac{24}{5} = 4.8 \]
Eliana should have arrived at \(t = 4.8\), but she mistakenly combined terms in step 3.
Now, looking at Eliana's steps:
1. **Step 3 (Where she messed up):**
Eliana wrote \(8 - 3t = -16\)
instead of \(8 + 16 = 5t\). She incorrectly combined the terms involving \(t\) on the right side.
2. **Property Used/Faulted:**
She didn’t apply the property correctly for balancing the equation when isolating \(t\).
Thus, Eliana's mistake happened in the third step where she combined the terms incorrectly. The correct process would involve moving all terms involving \(t\) to one side and the constants (8 and -16) to the other side correctly. The answer should be \(t = 4.8\), not \(t = 8\).