Solve the inequality 1 + 4c < 9 for c.
Check the final answer first, then review the worked steps.
Problem
Solve the inequality 1 + 4c < 9 for c.
Answer
\(c < 2\)
Step-by-step solution
1. Isolate the term with 'c': To begin, we want to get the term with 'c' by itself on one side of the inequality. We can do this by subtracting 1 from both sides of the inequality.
$$1 + 4c - 1 < 9 - 1$$
$$4c < 8$$
2. Solve for 'c': Now that we have the term with 'c' isolated, we can solve for 'c' by dividing both sides of the inequality by 4. Since 4 is a positive number, the direction of the inequality sign remains the same.
$$\frac{4c}{4} < \frac{8}{4}$$
$$c < 2$$