Solve n^2+4ngeqn^2-3n+1

$$n ^ { 2 } + 4 n \geq n ^ { 2 } - 3 n + 1$$

Solve for n

$$n\geq \frac{1}{7}$$

Solution Steps

Subtract n^{2} from both sides.

$$n^{2}+4n-n^{2}\geq -3n+1$$

Combine n^{2} and -n^{2} to get 0.

$$4n\geq -3n+1$$

Add 3n to both sides.

$$4n+3n\geq 1$$

Combine 4n and 3n to get 7n.

$$7n\geq 1$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$n\geq \frac{1}{7}$$