To solve the equation [tex]\( 5c - 2 = 3c \)[/tex] and find the value of [tex]\( 24c \)[/tex], we can follow these steps:
1. Start by isolating the variable [tex]\( c \)[/tex] in the given equation [tex]\( 5c - 2 = 3c \)[/tex].
2. Subtract [tex]\( 3c \)[/tex] from both sides to simplify:
[tex]\[
5c - 3c - 2 = 3c - 3c
\][/tex]
This simplifies to:
[tex]\[
2c - 2 = 0
\][/tex]
3. Add 2 to both sides to further isolate [tex]\( c \)[/tex]:
[tex]\[
2c - 2 + 2 = 0 + 2
\][/tex]
This simplifies to:
[tex]\[
2c = 2
\][/tex]
4. Divide both sides by 2 to solve for [tex]\( c \)[/tex]:
[tex]\[
\frac{2c}{2} = \frac{2}{2}
\][/tex]
This simplifies to:
[tex]\[
c = 1
\][/tex]
5. Now, we need to find the value of [tex]\( 24c \)[/tex]. Substitute [tex]\( c = 1 \)[/tex] into [tex]\( 24c \)[/tex]:
[tex]\[
24c = 24 \cdot 1 = 24
\][/tex]
Therefore, the value of [tex]\( 24c \)[/tex] is [tex]\(\boxed{24}\)[/tex].
