To solve the equation [tex]\( 4x - 3 + 5 = 2x + 7 - 8x \)[/tex], follow these steps:
1. Simplify both sides of the equation:
[tex]\[
4x - 3 + 5 = 2x + 7 - 8x
\][/tex]
Combine the constants and the like terms on each side:
[tex]\[
4x + 2 = 2x + 7 - 8x
\][/tex]
2. Combine like terms:
On the left side, [tex]\( 4x \)[/tex] remains the same, and the constants [tex]\( -3 + 5 \)[/tex] combine to give 2:
[tex]\[
4x + 2
\][/tex]
On the right side, [tex]\( 2x \)[/tex] and [tex]\( -8x \)[/tex] combine to give [tex]\( -6x \)[/tex]:
[tex]\[
2x + 7 - 8x = -6x + 7
\][/tex]
Now we have:
[tex]\[
4x + 2 = -6x + 7
\][/tex]
3. Isolate the variable [tex]\( x \)[/tex]:
To get all [tex]\( x \)[/tex]-terms on one side, add [tex]\( 6x \)[/tex] to both sides:
[tex]\[
4x + 6x + 2 = 7
\][/tex]
This simplifies to:
[tex]\[
10x + 2 = 7
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Subtract 2 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
10x = 5
\][/tex]
Then, divide both sides by 10 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5}{10} = \frac{1}{2}
\][/tex]
Thus, the solution to the equation [tex]\( 4x - 3 + 5 = 2x + 7 - 8x \)[/tex] is [tex]\( x = \frac{1}{2} \)[/tex].
The correct answer is:
[tex]\[ \boxed{x = \frac{1}{2}} \][/tex]
which corresponds to option B.
