To solve for [tex]\(24c\)[/tex] given the equation [tex]\(5c - 2 = 3c\)[/tex], we need to first find the value of [tex]\(c\)[/tex]. Here is the step-by-step solution:
1. Start with the given equation:
[tex]\[
5c - 2 = 3c
\][/tex]
2. To isolate [tex]\(c\)[/tex], we need to move all terms involving [tex]\(c\)[/tex] to one side of the equation. Subtract [tex]\(3c\)[/tex] from both sides:
[tex]\[
5c - 3c - 2 = 0
\][/tex]
3. Simplify the left side by combining like terms:
[tex]\[
2c - 2 = 0
\][/tex]
4. Next, isolate the term with [tex]\(c\)[/tex]. Add 2 to both sides of the equation:
[tex]\[
2c = 2
\][/tex]
5. Now, solve for [tex]\(c\)[/tex] by dividing both sides by 2:
[tex]\[
c = 1
\][/tex]
6. Having found that [tex]\(c = 1\)[/tex], we can now determine the value of [tex]\(24c\)[/tex]:
[tex]\[
24c = 24 \cdot 1 = 24
\][/tex]
Therefore, the value of [tex]\(24c\)[/tex] is [tex]\(24\)[/tex]. So the answer is:
[tex]\[
\boxed{24}
\][/tex]
