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What is the solution for [tex]$x$[/tex] in the equation?

[tex]4x - 3 + 5 = 2x + 7 - 8x[/tex]

A. [tex]$x = -\frac{1}{2}$[/tex]

B. [tex][tex]$x = \frac{1}{2}$[/tex][/tex]

C. [tex]$x = 2$[/tex]

D. [tex]$x = -2$[/tex]


Sagot :

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.