Part A: Circle the first mistake. $$ \begin{array}{l} ext { Part B: Find the correct solution. } \ \begin{array}{l} 6-x=5 x+30 \ -x-x\end{array} \ 6=4 x+30 \ -30-30 \ \frac{-24}{4}=\frac{4 x}{4} \ -6=x\end{array} $$

Question

Part A: Circle the first mistake. $$ \begin{array}{l}	ext { Part B: Find the correct solution. } \ \begin{array}{l} 6-x=5 x+30 \ -x-x\end{array} \ 6=4 x+30 \ -30-30 \ \frac{-24}{4}=\frac{4 x}{4} \ -6=x\end{array} $$

UpStudy AI · Accepted Answer

**Part A: Circle the First Mistake**

The first mistake occurs in the second step:

$$
6 - x = 5x + 30 \
\underline{-x - x} \quad \text{← Incorrect Step}
$$

**Explanation of the Mistake:**
In this step, the intention seems to be to combine like terms by subtracting $$ x $$ from both sides. However, subtracting $$ x $$ from both sides of the equation $$ 6 - x = 5x + 30 $$ should result in:

$$
6 - 2x = 5x + 30 - x \
6 - 2x = 4x + 30
$$

Instead, the step incorrectly simplifies to $$ 6 = 4x + 30 $$, neglecting the $$ -2x $$ term on the left side.

---

**Part B: Find the Correct Solution**

Let's solve the equation step-by-step correctly.

**Given Equation:**
$$
6 - x = 5x + 30
$$

**Step 1: Subtract $$ 5x $$ from both sides to get all $$ x $$-terms on one side.**
$$
6 - x - 5x = 5x + 30 - 5x \
6 - 6x = 30
$$

**Step 2: Subtract 6 from both sides to isolate the $$ x $$-term.**
$$
6 - 6x - 6 = 30 - 6 \
-6x = 24
$$

**Step 3: Divide both sides by $$ -6 $$ to solve for $$ x $$.**
$$
\frac{-6x}{-6} = \frac{24}{-6} \
x = -4
$$

**Solution:**
$$
x = -4
$$
**Part A: Circle the First Mistake** The first mistake is in the second step: $$ 6 - x = 5x + 30 \ \underline{-x - x} \quad \text{← Incorrect Step} $$ **Part B: Correct Solution** Solving the equation: $$ 6 - x = 5x + 30 \ 6 - 2x = 4x + 30 \ -2x - 4x = 30 - 6 \ -6x = 24 \ x = -4 $$ So, the correct solution is $$ x = -4 $$.

Part A: Circle the first mistake. \( \begin{array}{l}\text { Part B: Find the correct solution. } \\ \begin{array}{l} 6-x=5 x+30 \\ -x-x\end{array} \\ 6=4 x+30 \\ -30-30 \\ \frac{-24}{4}=\frac{4 x}{4} \\ -6=x\end{array} \)

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