To solve the inequality [tex]\( 4c - 6 \leq 3c - 2 \)[/tex], follow these steps:
1. Isolate the variable [tex]\( c \)[/tex]:
- Subtract [tex]\( 3c \)[/tex] from both sides of the inequality to eliminate [tex]\( c \)[/tex] on the right-hand side:
[tex]\[
4c - 6 - 3c \leq 3c - 2 - 3c
\][/tex]
- Simplify the expression:
[tex]\[
c - 6 \leq -2
\][/tex]
2. Add 6 to both sides of the inequality to isolate the variable [tex]\( c \)[/tex] on one side:
[tex]\[
c - 6 + 6 \leq -2 + 6
\][/tex]
Simplify the expression:
[tex]\[
c \leq 4
\][/tex]
3. Write the solution set in interval notation:
- The inequality [tex]\( c \leq 4 \)[/tex] includes all values of [tex]\( c \)[/tex] that are less than or equal to 4.
- In interval notation, this is written as:
[tex]\[
(-\infty, 4]
\][/tex]
Therefore, the solution set for the inequality [tex]\( 4c - 6 \leq 3c - 2 \)[/tex] in interval notation is [tex]\(\boxed{(-\infty, 4]}\)[/tex].
