Chapter 1

Solve each equation in Exercises \(1-14\) by factoring. $$7-7 x=(3 x+2)(x-1)$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(1,6]$$

Let \(x\) represent the number. Write each English phrase as an algebraic expression. Four times the sum of a number and 12

In Exercises \(1-16,\) solve and check each linear equation. $$ 16=3(x-1)-(x-7) $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(8-4 i)(-3+9 i)$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 9 x^{2}+3 x-2 \geq 0 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=x^{2}+2$$

Solve each radical equation in Check all proposed solutions. $$ \sqrt{x+10}=x-2 $$

Solve each equation in Exercises \(1-14\) by factoring. $$10 x-1=(2 x+1)^{2}$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(-2,4]$$

Let \(x\) represent the number. Write each English phrase as an algebraic expression. Five times the difference of a number and 6

In Exercises \(1-16,\) solve and check each linear equation. $$ 5 x-(2 x+2)=x+(3 x-5) $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(3+5 i)(3-5 i)$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 2 x^{2}+x<15 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=x-2$$

Solve each radical equation in Check all proposed solutions. $$ \sqrt{2 x+13}=x+7 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$3 x^{2}=27$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$[-5,2)$$

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. A number increased by 40 is equal to \(450 .\) Find the number.

In Exercises \(1-16,\) solve and check each linear equation. $$ \begin{array}{r} 25-[2+5 y-3(y+2)]= \\ -3(2 y-5)-[5(y-1)-3 y+3] \end{array} $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(2+7 i)(2-7 i)$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 6 x^{2}+x>1 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=x+2$$

Solve each radical equation in Check all proposed solutions. $$ \sqrt{6 x+1}=x-1 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$5 x^{2}=45$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$[-4,3)$$

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. The sum of a number and 29 is \(54 .\) Find the number.

In Exercises \(1-16,\) solve and check each linear equation. $$ \begin{aligned} 45-[4-2 y-4(y+7)] &=\\\ -4(1+3 y)-[4-3(y+2)-2(2 y-5)] \end{aligned} $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(-5+3 i)(-5-3 i)$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 4 x^{2}+7 x<-3 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=2 x+1$$

Solve each radical equation in Check all proposed solutions. $$ x-\sqrt{2 x+5}=5 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$5 x^{2}+1=51$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$[-3,1]$$

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Seven subtracted from five times a number is \(123 .\) Find the number.

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x}{3}=\frac{x}{2}-2 $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(-7-4 i)(-7+4 i)$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}+16 x<-5 $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=2 x-4$$

Solve each radical equation in Check all proposed solutions. $$ x-\sqrt{x+11}=1 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$3 x^{2}-1=47$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$[-2,5]$$

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Eight subtracted from six times a number is \(184 .\) Find the number.

Exercises \(17-30\) contain equations with constants in denominators. Solve each equation. $$ \frac{x}{5}=\frac{x}{6}+1 $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(2+3 i)^{2}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 5 x \leq 2-3 x^{2} $$

Graph each equation in Exercises \(13-28 .\) Let \(x=-3,-2,-1\) \(0,1,2,\) and 3. $$y=-\frac{1}{2} x$$

Solve each radical equation in Check all proposed solutions. $$ \sqrt{3 x}+10=x+4 $$

Solve each equation in Exercises \(15-26\) by the square root method. $$(x+2)^{2}=25$$

In Exercises 13-26, express each interval in terms of an inequality and graph the interval on a number line. $$(2, \infty)$$