Let's solve the given equation step-by-step to find the value of [tex]\( x \)[/tex] and determine which of the multiple choice options it matches.
The given equation is:
[tex]\[ 2(1 + 10x) = 52 \][/tex]
### Step 1: Distribute the 2
First, we distribute the 2 on the left side of the equation:
[tex]\[ 2 \cdot 1 + 2 \cdot 10x = 2 + 20x \][/tex]
So, the equation becomes:
[tex]\[ 2 + 20x = 52 \][/tex]
### Step 2: Isolate the term with [tex]\( x \)[/tex]
Next, we need to isolate the term that contains [tex]\( x \)[/tex]. To do this, we subtract 2 from both sides of the equation:
[tex]\[ 20x = 52 - 2 \][/tex]
[tex]\[ 20x = 50 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Now, we divide both sides of the equation by 20 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{50}{20} \][/tex]
### Step 4: Simplify the fraction
Simplify [tex]\(\frac{50}{20}\)[/tex]:
[tex]\[ x = \frac{50}{20} = \frac{50 \div 10}{20 \div 10} = \frac{5}{2} = 2.5 \][/tex]
Thus, [tex]\( x = 2.5 \)[/tex].
### Step 5: Convert [tex]\( x \)[/tex] to a fraction (if necessary)
For comparison with the given multiple choice options, let's note that [tex]\( x = 2.5 \)[/tex] is equivalent to [tex]\(\frac{5}{2}\)[/tex]. However, the options are provided as fractions, so the simplified version is essential.
### Step 6: Compare with given choices
Now we need to compare our value of [tex]\( x \)[/tex] with the given options:
1. [tex]\(\frac{51}{20} = 2.55\)[/tex]
2. [tex]\(\frac{49}{10} = 4.9\)[/tex]
3. [tex]\(\frac{50}{20} = 2.5\)[/tex]
4. [tex]\(\frac{26}{11} \approx 2.36\)[/tex]
Out of these, [tex]\(\frac{50}{20}\)[/tex] matches our [tex]\( x = 2.5 \)[/tex].
Therefore, the correct answer is:
Option 3: [tex]\(\frac{50}{20}\)[/tex].
