To solve the inequality [tex]\( 4c < 14 - 3c \)[/tex], let's go through the process step-by-step.
1. Combine like terms involving [tex]\( c \)[/tex]:
Start by moving all terms containing [tex]\( c \)[/tex] to one side of the inequality. We can accomplish this by adding [tex]\( 3c \)[/tex] to both sides of the inequality:
[tex]\[
4c + 3c < 14 - 3c + 3c
\][/tex]
Simplifying this, we get:
[tex]\[
7c < 14
\][/tex]
2. Isolate the variable [tex]\( c \)[/tex]:
Next, we need to isolate [tex]\( c \)[/tex] by dividing both sides of the inequality by 7:
[tex]\[
\frac{7c}{7} < \frac{14}{7}
\][/tex]
Simplifying this, we obtain:
[tex]\[
c < 2
\][/tex]
Thus, the solution to the inequality is [tex]\( c < 2 \)[/tex].
Since there are no specific domain restrictions noted for [tex]\( c \)[/tex], it can be any real number less than 2. Therefore, the solution in interval notation can be written as:
[tex]\[
(-\infty, 2)
\][/tex]
In summary, [tex]\( c \)[/tex] must be less than 2 for [tex]\( 4c < 14 - 3c \)[/tex] to hold true.
