Sure, let's go through the process of solving for [tex]\( x \)[/tex] from the given equation:
[tex]\[ 3x - 2y = 4 \][/tex]
### Step 1: Isolate the term involving [tex]\( x \)[/tex]
We want to get [tex]\( x \)[/tex] by itself on one side of the equation. To do this, we first add [tex]\( 2y \)[/tex] to both sides of the equation to move the term involving [tex]\( y \)[/tex] to the right side:
[tex]\[ 3x - 2y + 2y = 4 + 2y \][/tex]
This simplifies to:
[tex]\[ 3x = 4 + 2y \][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
Next, we need to isolate [tex]\( x \)[/tex] completely. Since [tex]\( x \)[/tex] is multiplied by 3, we divide both sides of the equation by 3:
[tex]\[ x = \frac{4 + 2y}{3} \][/tex]
This gives us the solution for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ \boxed{x = \frac{4 + 2y}{3}} \][/tex]
### Example with [tex]\( y = 1 \)[/tex]
To provide a concrete example, let's substitute [tex]\( y = 1 \)[/tex] into the equation and solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{4 + 2(1)}{3} \][/tex]
This simplifies to:
[tex]\[ x = \frac{4 + 2}{3} \][/tex]
[tex]\[ x = \frac{6}{3} \][/tex]
[tex]\[ x = 2 \][/tex]
So, if [tex]\( y = 1 \)[/tex], then [tex]\( x = 2 \)[/tex].
Therefore, from the provided equation [tex]\( 3x - 2y = 4 \)[/tex], the value of [tex]\( x \)[/tex] can be expressed as [tex]\( x = \frac{4 + 2y}{3} \)[/tex]. For the specific case where [tex]\( y = 1 \)[/tex], we find that [tex]\( x = 2 \)[/tex].
