Chapter 1

Find the test intervals of the inequality. \(x^{2}-25<0\)

Write an inequality that represents the interval. Then state whether the interval is bounded or unbounded. \([-1,5]\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(x^{3}-2 x^{2}-3 x=0\)

In Exercises 1-8, use the discriminant to determine the number of real solutions of the quadratic equation. \(4 x^{2}-4 x+1=0\)

In Exercises 1-10, write the quadratic equation in general form. $$ 2 x^{2}=3-5 x $$

In Exercises 1–10, write an algebraic expression for the verbal expression. The sum of two consecutive natural numbers

In Exercises 1-6, determine whether the equation is an identity or a conditional equation. $$ 2(x-1)=2 x-2 $$

Find the test intervals of the inequality. \(x^{2}-6 x+8>0\)

Write an inequality that represents the interval. Then state whether the interval is bounded or unbounded. \((2,10]\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(20 x^{3}-125 x=0\)

Use the discriminant to determine the number of real solutions of the quadratic equation. \(2 x^{2}-x-1=0\)

Write the quadratic equation in general form. $$ 4 x^{2}-2 x=9 $$

Write an algebraic expression for the verbal expression. The product of two natural numbers whose sum is 25.

Determine whether the equation is an identity or a conditional equation. $$ 3(x+2)=3 x+6 $$

Find the test intervals of the inequality. \(2 x^{2}+7 x+16 \geq 20\)

Write an inequality that represents the interval. Then state whether the interval is bounded or unbounded. \((11, \infty)\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(4 x^{4}-18 x^{2}=0\)

Use the discriminant to determine the number of real solutions of the quadratic equation. \(3 x^{2}+4 x+1=0\)

Write the quadratic equation in general form. $$ x^{2}=25 x $$

Write an algebraic expression for the verbal expression. The distance traveled in \(t\) hours by a car traveling at 50 miles per hour

Determine whether the equation is an identity or a conditional equation. $$ 2(x-1)=3 x+4 $$

Find the test intervals of the inequality. \(3 x^{2}-26 x+25 \leq 9\)

Write an inequality that represents the interval. Then state whether the interval is bounded or unbounded. \([-5, \infty)\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(2 x^{4}-15 x^{3}+18 x^{2}=0\)

Use the discriminant to determine the number of real solutions of the quadratic equation. \(x^{2}+2 x+4=0\)

Write the quadratic equation in general form. $$ 10 x^{2}=90 $$

Write an algebraic expression for the verbal expression. The travel time for a plane that is traveling at a rate of \(r\) miles per hour for 200 miles

Determine whether the equation is an identity or a conditional equation. $$ 3(x+2)=2 x+4 $$

Find the test intervals of the inequality. \(\frac{x-3}{x-1}<2\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(x^{4}-81=0\)

Use the discriminant to determine the number of real solutions of the quadratic equation. \(2 x^{2}-5 x=-5\)

Write the quadratic equation in general form. $$ (x-3)^{2}=2 $$

Write an algebraic expression for the verbal expression. Acid Solution The amount of acid in \(x\) gallons of a \(20 \%\) acid solution

Determine whether the equation is an identity or a conditional equation. $$ 2(x+1)=2 x+1 $$

Find the test intervals of the inequality. \(\frac{x-4}{2 x+3} \geq 1\)

Write an inequality that represents the interval. Then state whether the interval is bounded or unbounded. \((-\infty, 7]\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(x^{6}-64=0\)

Use the discriminant to determine the number of real solutions of the quadratic equation. \(3-6 x=-3 x^{2}\)

Write the quadratic equation in general form. $$ 12-3(x+7)^{2}=0 $$

Write an algebraic expression for the verbal expression. Discount The sale price of an item that is discounted by \(20 \%\) of its list price \(L\)

Determine whether the equation is an identity or a conditional equation. $$ 3(x+4)=3 x+4 $$

Solve the inequality. Then graph the solution set on the real number line. \(x^{2} \leq 9\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(5 x^{3}+30 x^{2}+45 x=0\)

Use the discriminant to determine the number of real solutions of the quadratic equation. \(\frac{1}{5} x^{2}+\frac{6}{5} x-8=0\)

Write the quadratic equation in general form. $$ x(x+2)=3 x^{2}+1 $$

Write an algebraic expression for the verbal expression. Geometry The perimeter of a rectangle whose width is \(x\) and whose length is twice the width

Solve the inequality. Then graph the solution set on the real number line. \(x^{2}<5\)

Find the real solution(s) of the polynomial equation. Check your solutions. \(9 x^{4}-24 x^{3}+16 x^{2}=0\)

Use the discriminant to determine the number of real solutions of the quadratic equation. \(\frac{1}{3} x^{2}-5 x+25=0\)

Write the quadratic equation in general form. $$ x(x+5)=2(x+5) $$