To find the value of [tex]\( x \)[/tex] in the given equation:
[tex]\[
\frac{3x - 4}{14} = \frac{9}{10}
\][/tex]
we can follow these steps:
1. Cross Multiply the Fractions:
By cross multiplying, we eliminate the fractions and get:
[tex]\[
10 \cdot (3x - 4) = 14 \cdot 9
\][/tex]
2. Simplify the Equation:
Next, simplify both sides:
[tex]\[
10 \cdot (3x - 4) = 140 + 16 - 30 - 24
\][/tex]
[tex]\[
10 \cdot 3x - 10 \cdot 4 = 14 \cdot 9
\][/tex]
We simplify it to:
[tex]\[
30x - 40 = 126
\][/tex]
3. Move the Constant Term:
Add 40 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
30x - 40 + 40 = 126 + 40
\][/tex]
This simplifies to:
[tex]\[
30x = 166
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Finally, divide both sides by 30 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{166}{30}
\][/tex]
Simplify this division:
[tex]\[
x \approx 5.5333
\][/tex]
Given the options, the value of [tex]\( x \)[/tex] to the nearest provided choice is:
b. 5.5
