\begin{tabular}{|lc}\hline SOLVING EQUATIONS \ \hline 1. & Distribute \ \hline 2. $$ \begin{array}{c} ext { Simplify Each Side } \ ext { by combining like terms }\end{array} $$ \ \hline 3. $$ \begin{array}{c} ext { Move Variables } \ ext { to one side }\end{array} $$ \ \hline 4. $$ \begin{array}{c} ext { Solve }\end{array} $$ \ \hline $$ \begin{array}{l} ext { Examples inverse operations }\end{array} $$ \ \hline \hline Directions: Solve each equation below. $$ \frac{10 x+17-(x-9)}{2}=3 x+1 $$ \ \hline\end{tabular}

Question

\begin{tabular}{|lc}\hline SOLVING EQUATIONS \ \hline 1. & Distribute \ \hline 2. $$ \begin{array}{c}	ext { Simplify Each Side } \ 	ext { by combining like terms }\end{array} $$ \ \hline 3. $$ \begin{array}{c}	ext { Move Variables } \ 	ext { to one side }\end{array} $$ \ \hline 4. $$ \begin{array}{c}	ext { Solve }\end{array} $$ \ \hline $$ \begin{array}{l}	ext { Examples inverse operations }\end{array} $$ \ \hline \hline Directions: Solve each equation below. $$ \frac{10 x+17-(x-9)}{2}=3 x+1 $$ \ \hline\end{tabular}

UpStudy AI · Accepted Answer

Certainly! Let's solve the equation step-by-step following the provided directions.

**Given Equation:**
$$
\frac{10x + 17 - (x - 9)}{2} = 3x + 1
$$

---

### **Step 1: Distribute**

First, distribute the negative sign inside the parentheses in the numerator:

$$
10x + 17 - (x - 9) = 10x + 17 - x + 9 = 9x + 26
$$

So, the equation becomes:

$$
\frac{9x + 26}{2} = 3x + 1
$$

---

### **Step 2: Simplify Each Side by Combining Like Terms**

The left side is already simplified after distribution. Next, eliminate the denominator by multiplying both sides of the equation by 2:

$$
2 \times \left( \frac{9x + 26}{2} \right) = 2 \times (3x + 1)
$$

This simplifies to:

$$
9x + 26 = 6x + 2
$$

---

### **Step 3: Move Variables to One Side**

To gather all the variable terms on one side, subtract $$6x$$ from both sides:

$$
9x - 6x + 26 = 6x - 6x + 2
$$

Which simplifies to:

$$
3x + 26 = 2
$$

---

### **Step 4: Solve**

Now, isolate $$x$$ by performing the following steps:

1. **Subtract 26 from both sides:**
   $$
   3x + 26 - 26 = 2 - 26
   $$
   $$
   3x = -24
   $$

2. **Divide both sides by 3:**
   $$
   \frac{3x}{3} = \frac{-24}{3}
   $$
   $$
   x = -8
   $$

---

### **Solution:**
$$
x = -8
$$
$$ x = -8 $$

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