To solve the equation [tex]\( 8x - 2 - 5x = 8 \)[/tex], follow these steps:
1. Combine like terms on the left side of the equation:
[tex]\( 8x \)[/tex] and [tex]\( -5x \)[/tex] are like terms. Subtract [tex]\( 5x \)[/tex] from [tex]\( 8x \)[/tex]:
[tex]\[
8x - 5x = 3x
\][/tex]
Now substitute back into the equation:
[tex]\[
3x - 2 = 8
\][/tex]
2. Isolate the term containing [tex]\( x \)[/tex]:
To isolate [tex]\( 3x \)[/tex], add 2 to both sides of the equation:
[tex]\[
3x - 2 + 2 = 8 + 2
\][/tex]
Simplify:
[tex]\[
3x = 10
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{10}{3}
\][/tex]
The value of [tex]\( x \)[/tex] is [tex]\( \frac{10}{3} \)[/tex].
4. Compare [tex]\( x \)[/tex] with the given options:
- Option A: [tex]\( 13 \)[/tex]
- Option B: [tex]\( \frac{21}{2} \)[/tex]
- Option C: [tex]\( \frac{31}{3} \)[/tex]
- Option D: [tex]\( 7 \)[/tex]
Convert the value [tex]\( \frac{10}{3} \)[/tex] to a decimal form for easier comparison:
[tex]\[
\frac{10}{3} \approx 3.3333
\][/tex]
After comparison with the options:
- Option A: 13 is incorrect.
- Option B: [tex]\( \frac{21}{2} = 10.5\)[/tex] is incorrect.
- Option C: [tex]\( \frac{31}{3} \approx 10.3333 \)[/tex] is incorrect.
- Option D: 7 is incorrect.
None of the provided options correctly matches [tex]\( x = \frac{10}{3} \)[/tex]. Therefore, there is no correct option given in the list provided.
