Chapter 2

Solve the equation (if possible). $$\frac{x-11}{x}=\frac{x-9}{x}+2$$

Solve the equation algebraically. Check your solution graphically. $$6 x+1=-9 x-8$$

Use a graphing utility to graph the equation and graphically approximate the values of \(x\) that satisfy the specified inequalities. Then solve each inequality algebraically. Equation \(y=2 x-3\) Inequalities (a) \(y \geq 1\) (b) \(y \leq 0\)

Find all solutions of the equation algebraically. Check your solutions. $$3 \sqrt{x-5}+\sqrt{x-1}=0$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$x^{2}-6 x+2=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$\frac{x-3}{3}=\frac{3 x-5}{2}$$

Perform the operation and write the result in standard form. $$4(3+5 i)$$

Solve the equation (if possible). $$\frac{1}{x-3}+\frac{1}{x+3}=\frac{10}{x^{2}-9}$$

Solve the equation algebraically. Check your solution graphically. $$3(x-3)=7 x+2$$

Use a graphing utility to graph the equation and graphically approximate the values of \(x\) that satisfy the specified inequalities. Then solve each inequality algebraically. Equation \(y=\frac{2}{3} x+1\) Inequalities (a) \(y \leq 5\) (b) \(y \geq 0\)

Find all solutions of the equation algebraically. Check your solutions. $$4 \sqrt{x-3}-\sqrt{6 x-17}=3$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$x^{2}+8 x+14=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$\frac{x-3}{25}=\frac{x-5}{12}$$

Perform the operation and write the result in standard form. $$-6(5-3 i)$$

Solve the equation (if possible). $$\frac{1}{x-2}+\frac{3}{x+3}=\frac{4}{x^{2}+x-6}$$

Solve the equation algebraically. Check your solution graphically. $$8 x^{2}-10 x-3=0$$

Use a graphing utility to graph the equation and graphically approximate the values of \(x\) that satisfy the specified inequalities. Then solve each inequality algebraically. Equation \(y=-3 x+8\) Inequalities (a) \(-1 \leq y \leq 3\) (b) \(y \leq 0\)

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$3 x^{1 / 3}+2 x^{2 / 3}=5$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$x^{2}-4 x+13=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$\frac{x-5}{4}+\frac{x}{2}=10$$

Perform the operation and write the result in standard form. $$(1+i)(3-2 i)$$

Solve the equation (if possible). $$\frac{1}{x}+\frac{2}{x-5}=0$$

Solve the equation algebraically. Check your solution graphically. $$10 x^{2}-23 x-5=0$$

Use a graphing utility to graph the equation and graphically approximate the values of \(x\) that satisfy the specified inequalities. Then solve each inequality algebraically. Equation \(y=-\frac{1}{2} x+2\) Inequalities (a) \(0 \leq y \leq 3\) (b) \(y \geq 0\)

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$9 t^{2 / 3}+24 t^{1 / 3}=-16$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$x^{2}-6 x+34=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$\frac{x-5}{10}-\frac{x-3}{5}=1$$

Perform the operation and write the result in standard form. $$(6-2 i)(2-3 i)$$

Solve the equation (if possible). $$3=2+\frac{2}{z+2}$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$|5 x|>10$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$(x+6)^{3 / 2}=1$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$x^{2}+8 x+32=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$(x+2)^{2}=x^{2}-6 x+1$$

Perform the operation and write the result in standard form. $$4 i(8+5 i)$$

Solve the equation (if possible). $$\frac{2}{(x-4)(x-2)}=\frac{1}{x-4}+\frac{2}{x-2}$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$(x-1)^{3 / 2}=8$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$\left|\frac{x}{2}\right| \leq 1$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$x^{2}+18 x+117=0$$

Solve the equation algebraically. Then write the equation in the form \(f(x)=0\) and use a graphing utility to verify the algebraic solution. $$(x+1)^{2}+2(x-2)=(x+1)(x-2)$$

Perform the operation and write the result in standard form. $$-3 i(6-i)$$

Solve the equation (if possible). $$\frac{2}{x(x-2)}+\frac{5}{x}=\frac{1}{x-2}$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$(x-9)^{2 / 3}=25$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$|x-7| \leq 6$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$-6+2 x-x^{2}=0$$

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form \(f(x)=0.1\) $$x^{3}+x+4=0$$

Perform the operation and write the result in standard form. $$(\sqrt{14}+\sqrt{10} i)(\sqrt{14}-\sqrt{10} i)$$

Solve the equation (if possible). $$\frac{3}{x^{2}-3 x}+\frac{4}{x}=\frac{1}{x-3}$$

Solving an Equation Involving Rational Exponents Find all solutions of the equation algebraically. Check your solutions. $$(x-7)^{2 / 3}=9$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solutions graphically. $$|x-20|>4$$

Solve the quadratic equation by completing the square. Verify your answer graphically. $$-x^{2}+6 x-16=0$$