91Ó°ÊÓ

Graph the function. Observe the points of intersection and shade the \(x\) -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation. $$ |x-1|>2 $$

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ x^{2}+4 x+7=0 $$

For the following exercises, graph the function. Observe the points of intersection and shade the \(x\) -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation. $$ |x-1|>2 $$

For the following exercises, solve the equation involving absolute value. $$ |2 x-1|-7=-2 $$

For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. Solve for \(f : \frac{1}{p}+\frac{1}{q}=\frac{1}{f}\)

Solve for \(f: \frac{1}{p}+\frac{1}{q}=\frac{1}{f}\)

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ 3 x^{2}+5 x-8=0 $$

Graph the function. Observe the points of intersection and shade the \(x\) -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation. $$ |x+3| \geq 5 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{2+3 i}{2-3 i} $$

For the following exercises, solve the equation involving absolute value. $$ |2 x+1|-2=-3 $$