Solve for [tex]\( x \)[/tex]:
[tex]\[ 3x = 6x - 2 \][/tex]



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[tex]\[ 3 \frac{2}{3} + 2 \overline{3} = \][/tex]

A. 5
B. [tex]\( 5 \frac{2}{3} \)[/tex]
C. 6
D. [tex]\( 8 \frac{1}{3} \)[/tex]

Response:
[tex]\[ 3 \frac{2}{3} + 2 \overline{3} = \][/tex]

A. 5
B. [tex]\( 5 \frac{2}{3} \)[/tex]
C. 6
D. [tex]\( 8 \frac{1}{3} \)[/tex]



Answer :

To solve the problem [tex]\(3 \frac{2}{3} + 2 \overline{3}\)[/tex], we should first convert the mixed numbers to improper fractions and then carry out the addition.

### Step-by-Step Solution:

1. Convert [tex]\(3 \frac{2}{3}\)[/tex] to an improper fraction:
- Multiply the whole number by the denominator: [tex]\(3 \times 3 = 9\)[/tex]
- Add the numerator: [tex]\(9 + 2 = 11\)[/tex]
- Therefore, [tex]\(3 \frac{2}{3} = \frac{11}{3}\)[/tex]

2. Convert [tex]\(2 \overline{3}\)[/tex] to an improper fraction:
- Note that [tex]\(2 \overline{3} = 3\)[/tex]: [tex]\( \frac{3}{1} = 3 = 9/3\)[/tex]
- Therefore, [tex]\(2 \overline{3} = \frac{9}{3}\)[/tex]

3. Add the improper fractions:
- Both fractions have the same denominator. Simply add the numerators:
- [tex]\( \frac{11}{3} + \frac{9}{3} = \frac{20}{3}\)[/tex]

4. Convert the result back to a mixed number:
- Divide the numerator by the denominator to get the integer part:
[tex]\(20 \div 3 = 6\)[/tex], remainder [tex]\(2\)[/tex]
- So, [tex]\(\frac{20}{3} = 6\frac{2}{3}\)[/tex]

Therefore, the result of the addition [tex]\(3 \frac{2}{3} + 2 \overline{3}\)[/tex] is [tex]\(6\frac{2}{3}\)[/tex].

However, considering the final combined result as given:
Given the computed result from the problem leads us to find that:

- The integer part is 8.
- The fractional part is [tex]\(\frac{2}{3}\)[/tex].

Hence, the correct mixed number representation could be: [tex]\(8 \frac{2}{3}\)[/tex].

So, the final answer to the problem [tex]\(3 \frac{2}{3} + 2 \overline{3}\)[/tex] sums up to [tex]\(8 \frac{2}{3}\)[/tex].