To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 6.75 + \frac{3}{8} x = 13 \frac{1}{4} \)[/tex], follow these detailed steps:
1. Convert the mixed number to a decimal:
- [tex]\( 13 \frac{1}{4} \)[/tex] can be written as [tex]\( 13 + \frac{1}{4} \)[/tex].
- [tex]\(\frac{1}{4}\)[/tex] is 0.25, so [tex]\( 13 \frac{1}{4} = 13 + 0.25 = 13.25 \)[/tex].
2. Rewrite the equation with decimal numbers:
[tex]\[ 6.75 + \frac{3}{8} x = 13.25 \][/tex]
3. Isolate the term involving [tex]\( x \)[/tex] on one side of the equation:
[tex]\[ \frac{3}{8} x = 13.25 - 6.75 \][/tex]
[tex]\[ \frac{3}{8} x = 6.5 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\( \frac{3}{8} \)[/tex]:
[tex]\[ x = 6.5 \div \frac{3}{8} \][/tex]
5. Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[ x = 6.5 \times \frac{8}{3} \][/tex]
6. Calculate the value:
[tex]\[ x = 6.5 \times \frac{8}{3} \][/tex]
[tex]\[ x = \frac{6.5 \times 8}{3} \][/tex]
[tex]\[ x = \frac{52}{3} \][/tex]
7. Simplify the fraction (if necessary):
- [tex]\(\frac{52}{3} = 17.333\overline{3} \)[/tex]
- In mixed number form, this is [tex]\( 17 \frac{1}{3} \)[/tex].
So, the value of [tex]\( x \)[/tex] is [tex]\( 17 \frac{1}{3} \)[/tex], which corresponds to one of the given choices.
Therefore, the answer is:
[tex]\[ \boxed{17 \frac{1}{3}} \][/tex]
