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Solve for [tex]\( x \)[/tex].
[tex]\[ 10x + 8 = 11x - 6 \][/tex]
A. [tex]\( x = 14 \)[/tex] B. [tex]\( x = -14 \)[/tex] C. [tex]\( x = 21 \)[/tex] D. [tex]\( x = -2 \)[/tex]
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex]:
The given equation is: [tex]\[
10x + 8 = 11x - 6
\][/tex]
### Step 1: Isolate the [tex]\( x \)[/tex]-terms on one side. First, we want to get all the [tex]\( x \)[/tex]-terms on one side of the equation and the constant terms on the other side.
Subtract [tex]\( 10x \)[/tex] from both sides to move the [tex]\( x \)[/tex]-terms to the right side: [tex]\[
10x + 8 - 10x = 11x - 6 - 10x
\][/tex] This simplifies to: [tex]\[
8 = x - 6
\][/tex]
### Step 2: Isolate [tex]\( x \)[/tex]. Next, we need to isolate [tex]\( x \)[/tex]. We do this by adding 6 to both sides of the equation: [tex]\[
8 + 6 = x - 6 + 6
\][/tex] This simplifies to: [tex]\[
14 = x
\][/tex]
### Step 3: Solution So, the solution to the equation is: [tex]\[
x = 14
\][/tex]
The correct answer is: [tex]\[ \boxed{14} \][/tex]
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