Let's solve the equation step-by-step.
We start with the equation given:
[tex]\[ 5c - 2 = 3c \][/tex]
1. Isolate the variable [tex]\( c \)[/tex]: We want to get [tex]\( c \)[/tex] by itself on one side of the equation. To do this, we first need to eliminate [tex]\( c \)[/tex] from one side. We'll subtract [tex]\( 3c \)[/tex] from both sides of the equation:
[tex]\[ 5c - 2 - 3c = 3c - 3c \][/tex]
This simplifies to:
[tex]\[ 2c - 2 = 0 \][/tex]
2. Solve for [tex]\( c \)[/tex]: Next, add 2 to both sides to isolate the term with [tex]\( c \)[/tex]:
[tex]\[ 2c - 2 + 2 = 0 + 2 \][/tex]
[tex]\[ 2c = 2 \][/tex]
Now, divide both sides by 2 to solve for [tex]\( c \)[/tex]:
[tex]\[ \frac{2c}{2} = \frac{2}{2} \][/tex]
[tex]\[ c = 1 \][/tex]
Now that we have found [tex]\( c = 1 \)[/tex], we need to find [tex]\( 24c \)[/tex].
3. Calculate [tex]\( 24c \)[/tex]: Substitute [tex]\( c \)[/tex] with 1 in the expression [tex]\( 24c \)[/tex]:
[tex]\[ 24c = 24 \times 1 \][/tex]
[tex]\[ 24c = 24 \][/tex]
Thus, the value of [tex]\( 24c \)[/tex] is 24.
Therefore, the correct answer is:
[tex]\[ \boxed{24} \][/tex]
