Chapter 1

Check all proposed solutions. $$ \sqrt{2 x+13}=x+7 $$

Solve and check linear equation. \(25-[2+5 y-3(y+2)]=\) \(-3(2 y-5)-[5(y-1)-3 y+3]\)

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

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

Find all values of \(x\) satisfying the given conditions. \(y_{1}=2.5, y_{2}=2 x+1, y_{3}=x,\) and the difference between 2 times \(y_{1}\) and 3 times \(y_{2}\) is 8 less than 4 times \(y_{3}.\)

Solve each equation in Exercises \(15-34\) by the square root property. $$ 5 x^{2}=45 $$

Check all proposed solutions. $$ \sqrt{6 x+1}=x-1 $$

Solve and check linear equation. \(45-[4-2 y-4(y+7)]=\) \(-4(1+3 y)-[4-3(y+2)-2(2 y-5)]\)

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

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

Find all values of \(x\) satisfying the given conditions. \(y_{1}=\frac{1}{x}, y_{2}=\frac{1}{2 x}, y_{3}=\frac{1}{x-1},\) and the sum of 3 times \(y_{1}\) and 4 times \(y_{2}\) is the product of 4 and \(y_{3}.\)

Solve each equation in Exercises \(15-34\) by the square root property. $$ 5 x^{2}+1=51 $$

Check all proposed solutions. $$ x-\sqrt{2 x+5}=5 $$

Contain linear equations with constants in denominators. Solve equation. \(\frac{x}{3}=\frac{x}{2}-2\)

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

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

Find all values of \(x\) satisfying the given conditions. \(y_{1}=\frac{1}{x}, y_{2}=\frac{1}{x^{2}-x}, y_{3}=\frac{1}{x-1},\) and the difference between 6 times \(y_{1}\) and 3 times \(y_{2}\) is the product of 7 and \(y_{3}.\)

Solve each equation in Exercises \(15-34\) by the square root property. $$ 3 x^{2}-1=47 $$

Check all proposed solutions. $$ x-\sqrt{x+11}=1 $$

Contain linear equations with constants in denominators. Solve equation. \(\frac{x}{5}=\frac{x}{6}+1\)

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

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

Solve each equation in Exercises \(15-34\) by the square root property. $$ 2 x^{2}-5=-55 $$

Check all proposed solutions. $$ \sqrt{2 x+19}-8=x $$

Contain linear equations with constants in denominators. Solve equation. \(20-\frac{x}{3}=\frac{x}{2}\)

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

In Exercises \(9-20,\) find each product and write the result in standard form. $$(5-2 i)^{2}$$

Solve each equation in Exercises \(15-34\) by the square root property. $$ 2 x^{2}-7=-15 $$

Check all proposed solutions. $$ \sqrt{2 x+15}-6=x $$

Contain linear equations with constants in denominators. Solve equation. \(\frac{x}{5}-\frac{1}{2}=\frac{x}{6}\)

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

In Exercises \(21-28,\) divide and express the result in standard form. $$ \frac{2}{3-i} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ (x+2)^{2}=25 $$

Check all proposed solutions. $$ \sqrt{3 x}+10=x+4 $$

Contain linear equations with constants in denominators. Solve equation. \(\frac{3 x}{5}=\frac{2 x}{3}+1\)

In Exercises \(21-28,\) divide and express the result in standard form. $$ \frac{3}{4+i} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ (x-3)^{2}=36 $$

Check all proposed solutions. $$ \sqrt{x}-3=x-9 $$

Contain linear equations with constants in denominators. Solve equation. \(\frac{x}{2}=\frac{3 x}{4}+5\)

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

Even as A mericans increasingly view a college education as essential for success, many believe that a college education is becoming less available to qualified students. Exercises are based on the data displayed by the graph. GRAPH CANNOT COPY. In \(2000,31 \%\) of U.S. adults viewed a college education as essential for success. For the period 2000 through 2010 , the percentage viewing a college education as essential for success increased on average by approximately 2.4 each year. If this trend continues, by which year will \(67 \%\) of all American adults view a college education as essential for success?

In Exercises \(21-28,\) divide and express the result in standard form. $$ \frac{2 i}{1+i} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ 3(x-4)^{2}=15 $$

Check all proposed solutions. $$ \sqrt{x+8}-\sqrt{x-4}=2 $$

Use graphs to find each set. $$[3, \infty) \cap(6, \infty)$$

Contain linear equations with constants in denominators. Solve equation. \(\frac{3 x}{5}-x=\frac{x}{10}-\frac{5}{2}\)

Even as A mericans increasingly view a college education as essential for success, many believe that a college education is becoming less available to qualified students. Exercises are based on the data displayed by the graph. GRAPH CANNOT COPY. The data displayed by the graph at the bottom of the previous page indicate that in \(2000,45 \%\) of U.S. adults believed most qualified students get to attend college. For the period from 2000 through \(2010,\) the percentage who believed that a college education is available to most qualified students decreased by approximately 1.7 each year. If this trend continues, by which year will only \(11 \%\) of all American adults believe that most qualified students get to attend college?

In Exercises \(21-28,\) divide and express the result in standard form. $$ \frac{5 i}{2-i} $$

Solve each equation in Exercises \(15-34\) by the square root property. $$ 3(x+4)^{2}=21 $$

Check all proposed solutions. $$ \sqrt{x+5}-\sqrt{x-3}=2 $$