To solve the equation [tex]\( 5x - 6 = 3x + 10 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Isolate the variable [tex]\( x \)[/tex]:
- Start by moving all terms involving [tex]\( x \)[/tex] to one side of the equation.
- Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[
5x - 6 - 3x = 3x + 10 - 3x
\][/tex]
Simplifying this, we get:
[tex]\[
2x - 6 = 10
\][/tex]
2. Isolate [tex]\( x \)[/tex] further:
- Next, move the constant term on the left side to the right side.
- Add 6 to both sides:
[tex]\[
2x - 6 + 6 = 10 + 6
\][/tex]
Simplifying this, we get:
[tex]\[
2x = 16
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{2x}{2} = \frac{16}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 8
\][/tex]
So, the solution for the equation [tex]\( 5x - 6 = 3x + 10 \)[/tex] is [tex]\( x = 8 \)[/tex].
Comparing this with the provided options:
- [tex]\( x = 0.5 \)[/tex]
- [tex]\( x = 1 \)[/tex]
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 8 \)[/tex]
We see that the correct option is [tex]\( x = 8 \)[/tex].
