To solve the equation [tex]\( 5x - 6 = 3x + 10 \)[/tex] for [tex]\( x \)[/tex], follow these detailed steps:
1. Start with the given equation:
[tex]\[
5x - 6 = 3x + 10
\][/tex]
2. Move all terms containing [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side:
[tex]\[
5x - 3x = 10 + 6
\][/tex]
3. Simplify both sides of the equation:
[tex]\[
2x = 16
\][/tex]
4. Solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[
x = \frac{16}{2}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = 8
\][/tex]
So, the value of [tex]\( x \)[/tex] that satisfies the equation is [tex]\( x = 8 \)[/tex]. This is the correct answer from the given options:
- [tex]\( x = 0.5 \)[/tex]
- [tex]\( x = 1 \)[/tex]
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 8 \)[/tex]
Therefore, the solution is [tex]\( x = 8 \)[/tex].
