Chapter 1

Express each interval in set-builder notation and graph the interval on a number line. $$(3, \infty)$$

By factoring and then using the zero-product principle. $$ 9 y^{3}+8=4 y+18 y^{2} $$

Use the five-step strategy for solving word problems to find the number or numbers described in Exercises. \(70 \%\) of what number is \(252 ?\)

Solve and check linear equation. \(13 x+14=12 x-5\)

In Exercises \(1-12\), plot the given point in a rectangular coordinate system. $$ (3,-2) $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$-3 i(7 i-5)$$

Solve each equation in Exercises \(1-14\) by factoring. $$ 3 x^{2}+12 x=0 $$

Express each interval in set-builder notation and graph the interval on a number line. $$[-3, \infty)$$

Use the five-step strategy for solving word problems to find the number or numbers described in Exercises. One number exceeds another by \(26 .\) The sum of the numbers is \(64 .\) What are the numbers?

By factoring and then using the zero-product principle. $$ 2 x^{4}=16 x $$

Solve and check linear equation. \(3(x-2)+7=2(x+5)\)

In Exercises \(1-12\), plot the given point in a rectangular coordinate system. $$ (-4,0) $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$-8 i(2 i-7)$$

Solve each equation in Exercises \(1-14\) by factoring. $$ 5 x^{2}-20 x=0 $$

Use the five-step strategy for solving word problems to find the number or numbers described in Exercises. One number exceeds another by \(24 .\) The sum of the numbers is \(58 .\) What are the numbers?

Express each interval in set-builder notation and graph the interval on a number line. $$[-5, \infty)$$

By factoring and then using the zero-product principle. $$ 3 x^{4}=81 x $$

Solve and check linear equation. \(2(x-1)+3=x-3(x+1)\)

In Exercises \(1-12\), plot the given point in a rectangular coordinate system. $$ (0,-3) $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(-5+4 i)(3+i)$$

Solve each equation in Exercises \(1-14\) by factoring. $$ 2 x(x-3)=5 x^{2}-7 x $$

Find all values of \(x\) satisfying the given conditions. \(y_{1}=13 x-4, y_{2}=5 x+10,\) and \(y_{1}\) exceeds \(y_{2}\) by 2.

Express each interval in set-builder notation and graph the interval on a number line. $$(-\infty, 3)$$

Check all proposed solutions. \(\sqrt{3 x+18}=x\)

Solve and check linear equation. \(3(x-4)-4(x-3)=x+3-(x-2)\)

In Exercises \(1-12\), plot the given point in a rectangular coordinate system. $$ \left(\frac{2}{2},-\frac{3}{2}\right) $$

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

Solve each equation in Exercises \(1-14\) by factoring. $$ 16 x(x-2)=8 x-25 $$

Find all values of \(x\) satisfying the given conditions. \(y_{1}=10 x+6, y_{2}=12 x-7,\) and \(y_{1}\) exceeds \(y_{2}\) by 3.

Express each interval in set-builder notation and graph the interval on a number line. $$(-\infty, 2)$$

Check all proposed solutions. $$ \sqrt{20-8 x}=x $$

Solve and check linear equation. \(2-(7 x+5)=13-3 x\)

In Exercises \(1-12\), plot the given point in a rectangular coordinate system. $$ \left(-\frac{5}{2}, \frac{3}{2}\right) $$

In Exercises \(9-20,\) find each product and write the result in standard form. $$(7-5 i)(-2-3 i)$$

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

Find all values of \(x\) satisfying the given conditions. \(y_{1}=10(2 x-1), y_{2}=2 x+1,\) and \(y_{1}\) is 14 more than 8 times \(y_{2}.\)

Express each interval in set-builder notation and graph the interval on a number line. $$(-\infty, 5.5)$$

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

Solve and check linear equation. \(16=3(x-1)-(x-7)\)

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

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

Find all values of \(x\) satisfying the given conditions. \(y_{1}=9(3 x-5), y_{2}=3 x-1,\) and \(y_{1}\) is 51 less than 12 times \(y_{2}.\)

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

Check all proposed solutions. $$ \sqrt{x+10}=x-2 $$

Express each interval in set-builder notation and graph the interval on a number line. $$(-\infty, 3.5]$$

Solve and check linear equation. \(5 x-(2 x+2)=x+(3 x-5)\)

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

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

Find all values of \(x\) satisfying the given conditions. \(y_{1}=2 x+6, y_{2}=x+8, y_{3}=x,\) and the difference between 3 times \(y_{1}\) and 5 times \(y_{2}\) is 22 less than \(y_{3}.\)

Solve each equation in Exercises \(15-34\) by the square root property. $$ 3 x^{2}=27 $$