To determine the value of [tex]\( 24c \)[/tex] given the equation [tex]\( 5c - 2 = 3c \)[/tex], let's go step by step.
1. Initial Equation: We start with the equation:
[tex]\[
5c - 2 = 3c
\][/tex]
2. Isolate [tex]\( c \)[/tex]: To solve for [tex]\( c \)[/tex], we first get all the terms involving [tex]\( c \)[/tex] on one side of the equation. Subtract [tex]\( 3c \)[/tex] from both sides:
[tex]\[
5c - 3c - 2 = 3c - 3c
\][/tex]
3. Simplify: This simplifies to:
[tex]\[
2c - 2 = 0
\][/tex]
4. Isolate [tex]\( c \)[/tex] Further: Next, we add 2 to both sides of the equation to isolate the term involving [tex]\( c \)[/tex]:
[tex]\[
2c - 2 + 2 = 0 + 2
\][/tex]
[tex]\[
2c = 2
\][/tex]
5. Solve for [tex]\( c \)[/tex]: Finally, we divide both sides by 2:
[tex]\[
c = \frac{2}{2}
\][/tex]
[tex]\[
c = 1
\][/tex]
6. Calculate [tex]\( 24c \)[/tex]: Now that we have [tex]\( c = 1 \)[/tex], we substitute this value into [tex]\( 24c \)[/tex]:
[tex]\[
24c = 24 \times 1 = 24
\][/tex]
Therefore, the value of [tex]\( 24c \)[/tex] is [tex]\( 24 \)[/tex]. The correct answer is [tex]\( 24 \)[/tex].
