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?

Answer 1

Let’s carefully go through each step of Eliana’s work to find out if she correctly solved the equation \( 3.2 + 2(2.4 - 2t) = -16 + t \).

1. **Starting with the original equation:**
\[
3.2 + 2(2.4 - 2t) = -16 + t
\]

2. **Distributing the \( 2 \) in \( 2(2.4 - 2t) \):**
\[
2 \cdot 2.4 - 2 \cdot 2t = 4.8 - 4t
\]
Thus, the equation becomes:
\[
3.2 + 4.8 - 4t = -16 + t
\]

3. **Combining like terms on the left side:**
\[
3.2 + 4.8 = 8
\]
So the equation now is:
\[
8 - 4t = -16 + t
\]
This is the same as Eliana's Step 1.

4. **Rearranging the equation:**
We can move \( t \) to the left and \( 8 \) to the right:
\[
8 + 16 = t + 4t
\]
This simplifies to:
\[
24 = 5t \quad \text{or} \quad 8 - 4t = -16 + t
\]

5. **Continuing with Eliana's work:**
In Step 2, she wrote:
\[
8 - 4t = -16 + t
\]
(correct so far)

6. **To isolate \( t \): Add \( 4t \) and add \( 16 \) to both sides:**
\[
8 + 16 = t + 4t
\]
This gives:
\[
24 = 5t
\]

7. **Solving for \( t \):**
\[
t = \frac{24}{5} = 4.8
\]

From here we can see that Eliana's final value for \( t \) was found to be \( 8 \), which is incorrect.

Thus, Eliana did **not** solve the equation correctly. The correct solution gives \( t = 4.8 \).