To solve the given equation [tex]\(5c - 2 = 3c\)[/tex] and find the value of [tex]\(24c\)[/tex], follow these steps:
1. Isolate the variable [tex]\(c\)[/tex]:
[tex]\[
5c - 2 = 3c
\][/tex]
2. Subtract [tex]\(3c\)[/tex] from both sides to get all terms involving [tex]\(c\)[/tex] on one side:
[tex]\[
5c - 3c - 2 = 3c - 3c
\][/tex]
[tex]\[
2c - 2 = 0
\][/tex]
3. Add 2 to both sides to remove the constant term on the left side:
[tex]\[
2c - 2 + 2 = 0 + 2
\][/tex]
[tex]\[
2c = 2
\][/tex]
4. Divide both sides by 2 to solve for [tex]\(c\)[/tex]:
[tex]\[
\frac{2c}{2} = \frac{2}{2}
\][/tex]
[tex]\[
c = 1
\][/tex]
5. Now that we have the value of [tex]\(c\)[/tex], we need to find [tex]\(24c\)[/tex]:
[tex]\[
24c = 24 \times 1
\][/tex]
[tex]\[
24c = 24
\][/tex]
Therefore, the value of [tex]\(24c\)[/tex] is [tex]\(\boxed{24}\)[/tex].
