To solve for [tex]\( x \)[/tex] in the equation [tex]\( 3x - 1 = 27 \)[/tex], we can follow these steps:
1. Isolate the term with [tex]\( x \)[/tex]: The original equation is
[tex]\[
3x - 1 = 27
\][/tex]
We need to isolate [tex]\( 3x \)[/tex], so we add 1 to both sides:
[tex]\[
3x - 1 + 1 = 27 + 1
\][/tex]
Simplifying this, we get:
[tex]\[
3x = 28
\][/tex]
2. Solve for [tex]\( x \)[/tex]: To find [tex]\( x \)[/tex], we need to divide both sides of the equation by 3:
[tex]\[
x = \frac{28}{3}
\][/tex]
This gives us:
[tex]\[
x = \frac{28}{3} \approx 9.3333
\][/tex]
So, one of our solutions for [tex]\( x \)[/tex] is [tex]\( \frac{28}{3} \)[/tex].
Now let's check the other possible values of [tex]\( x \)[/tex] given in the options:
- Option 1: [tex]\( x = 10 \)[/tex]
To verify this, plug [tex]\( x = 10 \)[/tex] into the original equation:
[tex]\[
3(10) - 1 = 30 - 1 = 29 \neq 27
\][/tex]
This does not satisfy the original equation, so [tex]\( x = 10 \)[/tex] is not a valid solution.
- Option 2: [tex]\( x = \frac{28}{3} \)[/tex]
We have already verified that [tex]\( x = \frac{28}{3} \)[/tex] is a solution.
- Option 3: [tex]\( x = \frac{26}{3} \)[/tex]
To check this value, plug [tex]\( x = \frac{26}{3} \)[/tex] into the original equation:
[tex]\[
3 \left(\frac{26}{3}\right) - 1 = 26 - 1 = 25 \neq 27
\][/tex]
This does not satisfy the original equation, so [tex]\( x = \frac{26}{3} \)[/tex] is not a valid solution.
In conclusion, the correct solution is:
[tex]\[
x = \frac{28}{3} \approx 9.3333
\][/tex]
