Certainly! Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
Given the equation:
[tex]\[ 4(x - 3) = 3(x - 2) - 5 \][/tex]
First, we need to distribute the constants inside the parentheses:
[tex]\[ 4(x - 3) = 4x - 12 \][/tex]
[tex]\[ 3(x - 2) - 5 = 3x - 6 - 5 \][/tex]
Simplify the right-hand side of the equation:
[tex]\[ 3x - 6 - 5 = 3x - 11 \][/tex]
Now our equation is transformed to:
[tex]\[ 4x - 12 = 3x - 11 \][/tex]
Next, we need to get all terms involving [tex]\( x \)[/tex] on one side of the equation and the constant terms on the other side. Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[ 4x - 3x - 12 = -11 \][/tex]
[tex]\[ x - 12 = -11 \][/tex]
Then, add 12 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x - 12 + 12 = -11 + 12 \][/tex]
[tex]\[ x = 1 \][/tex]
So, the value of [tex]\( x \)[/tex] is:
[tex]\[ x = 1 \][/tex]
Therefore, the correct answer is:
C. 1
