Chapter 1

Solve equation by factoring. $$ 4 x^{2}-13 x=-3 $$

A new car worth \(\$ 45,000\) is depreciating in value by \(\$ 5000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 10,000\). c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

Solve and check each linear equation. $$13 x+14=12 x-5$$

Add or subtract as indicated and write the result in standard form. $$ 15 i-(12-11 i) $$

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

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$2 x^{4}=16 x$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ [-3, \infty) $$

Solve equation by factoring. $$ 3 x^{2}+12 x=0 $$

You are choosing between two health clubs. Club A offers membership for a fee of \(\$ 40\) plus a monthly fee of \(\$ 25 .\) Club \(\mathrm{B}\) offers membership for a fee of \(\$ 15\) plus a monthly fee of \(\$ 30\). After how many months will the total cost at each health club be the same? What will be the total cost for each club?

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

Find each product and write the result in standard form. $$ -3 i(7 i-5) $$

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

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$3 x^{4}=81 x$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ [-5, x) $$

Solve equation by factoring. $$ 5 x^{2}-20 x=0 $$

You need to rent a rug cleaner. Company A will rent the machine you need for \(\$ 22\) plus \(\$ 6\) per hour. Company \(B\) will rent the same machine for \(\$ 28\) plus \(\$ 4\) per hour. After how many hours of use will the total amount spent at each company be the same? What will be the total amount spent at each company?

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

Find each product and write the result in standard form. $$ -8 i(2 i-7) $$

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

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{3 x+18}=x$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (-\infty, 3) $$

Solve equation by factoring. $$ 2 x(x-3)=5 x^{2}-7 x $$

The bus fare in a city is \(\$ 1.25 .\) People who use the bus have the option of purchasing a monthly discount pass for \(\$ 15.00 .\) With the discount pass, the fare is reduced to \(\$ 0.75 .\) Determine the number of times in a month the bus must be used so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

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

Find each product and write the result in standard form. $$ (-5+4 i)(3+i) $$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$ \left(\frac{7}{2},-\frac{3}{2}\right) $$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{20-8 x}=x$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (-\infty, 2) $$

Solve equation by factoring. $$ 16 x(x-2)=8 x-25 $$

A discount pass for a bridge costs \(\$ 30\) per month. The toll for the bridge is normally \(\$ 5.00,\) but it is reduced to \(\$ 3.50\) for people who have purchased the discount pass. Determine the number of times in a month the bridge must be crossed so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

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

Find each product and write the result in standard form. $$ (-4-8 i)(3+i) $$

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

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $$\sqrt{x+3}=x-3$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (-\infty, 5.5) $$

Solve equation by factoring. $$ 7-7 x=(3 x+2)(x-1) $$

In \(2010,\) there were \(13,300\) students at college \(A,\) with a projected enrollment increase of 1000 students per year. In the same year, there \(26,800\) students at college \(B,\) with a projected enrollment decline of 500 students per year. a. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time? b. Use the following table to check your work in part (a) numerically. What equations were entered for \(Y_{1}\) and \(Y_{2}\) to obtain this table?

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

Find each product and write the result in standard form. $$ (7-5 i)(-2-3 i) $$

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 Exercises 11–30. Check all proposed solutions. $$\sqrt{x+10}=x-2$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (-\infty, 3.5] $$

Solve equation by factoring. $$ 10 x-1=(2 x+1)^{2} $$

In \(2000,\) the population of Greece was \(10,600,000,\) with projections of a population decrease of \(28,000\) people per year. In the same year, the population of Belgium was \(10,200,000,\) with projections of a population decrease of \(12,000\) people per year. (Source: United Nations) According to these projections, when will the two countries have the same population? What will be the population at that time?

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

Find each product and write the result in standard form. $$ (8-4 i)(-3+9 i) $$

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 Exercises 11–30. Check all proposed solutions. $$\sqrt{2 x+13}=x+7$$

Solve equation by the square root property. $$ 3 x^{2}=27 $$

After a \(20 \%\) reduction, you purchase a television for \(\$ 336\) What was the television's price before the reduction?