Question

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Suzie solved the equation 9x−5=14(16x+60)
using the following steps:

1) Distribute 1/4 to get 9x−5=4x+60


2) Use subtraction property of equality to move 4x to get 5x−5=60


3) Use addition property of equality to move 5 and get 5x=65


4) Use division property of equality to get x=13


Determine if Suzie solved correctly - if not, identify which step was the mistake.

(1 point)
Responses

Suzie solved the problem correctly
Suzie solved the problem correctly

Suzie made a mistake on Step 2 - she should have used the addition property instead
Suzie made a mistake on Step 2 - she should have used the addition property instead

Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well
Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well

Suzie made a mistake on Step 4 - she divided incorrectly

Answer 1

Let's analyze Suzie's steps to see if she solved the equation correctly.

The original equation is:

\[ 9x - 5 = 14(16x + 60) \]

**Step 1: Distribute 14 to (16x + 60)**

Here, Suzie incorrectly stated that she distributed \( \frac{1}{4} \). The correct distribution of 14 should be:

\[ 14 \cdot 16x + 14 \cdot 60 = 224x + 840 \]

Thus, the equation should be:

\[ 9x - 5 = 224x + 840 \]

**Step 2: Move 224x to the left side.**

Using the subtraction property of equality:

\[ 9x - 224x - 5 = 840 \]
\[ -215x - 5 = 840 \]

**Step 3: Move -5 to the right side using the addition property of equality.**

\[ -215x = 840 + 5 \]
\[ -215x = 845 \]

**Step 4: Divide by -215.**

\[ x = \frac{845}{-215} \]
\[ x = -\frac{845}{215} \] (This simplification would give a final answer)

Since Suzie made an error in Step 1, her entire following solution is based on that mistake.

Upon review of her original steps, we conclude:
- **Suzie made a mistake on Step 1 — she should have distributed 14 to both terms in the parentheses.**

So the correct response is:

**Suzie made a mistake on Step 1 - she should have distributed the 1/4 to 60 as well.** (This option slightly misstates what should be 14, but combines distribution works).