Chapter 2

Find the slope-intercept form for the line satisfying the conditions. Passing through \((-2,4)\) and perpendicular to the line passing through \(\left(-5, \frac{1}{2}\right)\) and \(\left(-3, \frac{2}{3}\right)\)

Solve the equation (a) graphically, (b) numerically, and (c) symbolically. Then solve the nelated inequality. $$|4 x-7|=5, \quad|4 x-7| \geq 5$$

Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. $$ 0.5(3 x-1)+0.5 x=2 x-0.5 $$

Find the slope-intercept form for the line satisfying the conditions. Passing through \(\left(\frac{3}{4}, \frac{1}{4}\right)\) and perpendicular to the line passing through \((-3,-5)\) and \((-4,0)\)

Solve the equation symbolically. Then solve the related inequality. $$|2.1 x-0.7|=2.4, \quad|2.1 x-0.7| \geq 2.4$$

Find an equation of the line satisfying the conditions. Vertical, passing through \((-5,6)\)

Exercises \(49-54:\) Write a formula for a linear function that models the situation. Choose both an appropriate name and an appropriate variable for the function. State what the input variable represents and the domain of the function. Assume that the domain is an interval of the real numbers. U.S. Homes with Internet In 2006 about \(68 \%\) of U.S. homes had Internet access. This percentage was expected to increase, on average, by 1.5 percentage points per year for the next 4 years. (Source: 2007 Digital Future Report)

Solve the equation symbolically. Then solve the related inequality. $$\left|\frac{1}{2} x-\frac{3}{4}\right|=\frac{7}{4}, \quad\left|\frac{1}{2^{x}}-\frac{3}{4}\right| \leq \frac{7}{4}$$

Find an equation of the line satisfying the conditions. Vertical, passing through \((1.95,10.7)\)

Exercises \(49-54:\) Write a formula for a linear function that models the situation. Choose both an appropriate name and an appropriate variable for the function. State what the input variable represents and the domain of the function. Assume that the domain is an interval of the real numbers. U.S. Cell Phones In 2005 there were about 208 million U.S. cell phone subscribers. This number was expected to increase, on average, by 20 million per year for the next 3 years. (Source: CTIA Industry Survey)

Solve the equation symbolically. Then solve the related inequality. $$|3 x|+5=6, \quad|3 x|+5>6$$

Find an equation of the line satisfying the conditions. Horizontal, passing through \((-5,6)\)

Use the \(x\) -intercept method to solve the inequality. Write the solution set in set-builder or interval notation. Then solve the inequality symbolically. $$ x-3 \leq \frac{1}{2} x-2 $$

Solve the equation symbolically. Then solve the related inequality. $$|x|-10=25, \quad|x|-10<25$$

Find an equation of the line satisfying the conditions. Horizontal, passing through \((1.95,10.7)\)

Use the \(x\) -intercept method to solve the inequality. Write the solution set in set-builder or interval notation. Then solve the inequality symbolically. $$ x-2 \leq \frac{1}{3} x $$

Exercises \(49-54:\) Write a formula for a linear function that models the situation. Choose both an appropriate name and an appropriate variable for the function. State what the input variable represents and the domain of the function. Assume that the domain is an interval of the real numbers. Speed of a Car \(\quad\) A car is traveling at 30 miles per hour, and then it begins to slow down at a constant rate of 6 miles per hour every 4 seconds.

Exercises \(53-58\) : Use the intersection-of-graphs method to solve the equation. Then solve symbolically.) x + 4 = 1 - 2x

Find an equation of the line satisfying the conditions. Perpendicular to \(y=15,\) passing through \((4,-9)\)

Use the \(x\) -intercept method to solve the inequality. Write the solution set in set-builder or interval notation. Then solve the inequality symbolically. $$ 2-x<3 x-2 $$

Exercises \(49-54:\) Write a formula for a linear function that models the situation. Choose both an appropriate name and an appropriate variable for the function. State what the input variable represents and the domain of the function. Assume that the domain is an interval of the real numbers. Population Density In 1900 the average number of people per square mile in the United States was \(21.5,\) and it increased, on average, by 5.81 people every 10 years until 2000 . (Source: Bureau of the Census.)

Use the intersection-of-graphs method to solve the equation. Then solve symbolically. 2x = 3x - 1

Find an equation of the line satisfying the conditions. Perpendicular to \(x=15\), passing through \((1.6,-9.5)\)

Use the \(x\) -intercept method to solve the inequality. Write the solution set in set-builder or interval notation. Then solve the inequality symbolically. $$ \frac{1}{2} x+1>\frac{3}{2} x-1 $$

Use the intersection-of-graphs method to solve the equation. Then solve symbolically. -x + 4 = 3x

Solve the inequality. Write the solution in interval notation. $$|3 x-1|<8$$

Find an equation of the line satisfying the conditions. Parallel to \(x=4.5,\) passing through \((19,5.5)\)

Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. $$ 5 x-4>10 $$

Exercises \(49-54:\) Write a formula for a linear function that models the situation. Choose both an appropriate name and an appropriate variable for the function. State what the input variable represents and the domain of the function. Assume that the domain is an interval of the real numbers. Draining a Water Tank A 300 -gallon tank is initially full of water and is being drained at a rate of 10 gallons per minute. (a) Write a formula for a function \(W\) that gives the number of gallons of water in the tank after \(t\) minutes. (b) How much water is in the tank after 7 minutes? (c) Graph \(W\) and identify and interpret the intercepts. (d) Find the domain of \(W\).

Use the intersection-of-graphs method to solve the equation. Then solve symbolically. 1-2x=x+4

Solve the inequality. Write the solution in interval notation. $$|15-x|<7$$

Find an equation of the line satisfying the conditions. Parallel to \(y=-2.5,\) passing through \((1985,67)\)

Fulling a Tank A 500 -gallon tank initially contains 200 gallons of fuel oil. A pump is filling the tank at a rate of 6 gallons per minute. (a) Write a formula for a linear function \(f\) that models the number of gallons of fuel oil in the tank after \(x\) minutes. (b) Graph \(f\). What is an appropriate domain for \(f ?\) (c) Identify the \(y\) -intercept and interpret it. (d) Does the \(x\) -intercept of the graph of \(f\) have any physical meaning in this problem? Explain.

Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. $$ -3 x+6 \leq 9 $$

Use the intersection-of-graphs method to solve the equation. Then solve symbolically. 2(x - 1) - 2 = x

Solve the inequality. Write the solution in interval notation. $$|7-4 x| \leq 11$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. \(4 x-5 y=20\)

HIV Infections In 2006 there were 40 million people worldwide who had been infected with HIV. At that time the infection rate was 4.3 million people per year. (Source: United Nations AIDS and World Health Organization.) (a) Write a formula for a linear function \(f\) that models the total number of people in millions who were infected with HIV \(x\) years after 2006 (b) Estimate the number of people who may have been infected by the year 2012 .

Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. $$ -2(x-1990)+55 \geq 60 $$

Use the intersection-of-graphs method to solve the equation. Then solve symbolically. -(x + 1) - 2 = 2x

Solve the inequality. Write the solution in interval notation. $$|-3 x+1| \leq 5$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. \(-3 x-5 y=15\)

Birth Rate In 1990 the number of births per 1000 people in the United States was 16.7 and decreasing at 0.21 birth per 1000 people each year. (Source: National Center for Health Statistics.) (a) Write a formula for a linear function \(f\) that models the birth rate \(x\) years after 1990 . (b) Estimate the birth rate in 2003 and compare the estimate to the actual value of 14 (IMAGE CANT COPY)

Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. $$ \sqrt{2} x>10.5-13.7 x $$

Exercises \(59-66:\) Solve the linear equation with the intersection-of-graphs method. Approximate the solution to the nearest thousandth whenever appropriate. $$ 5 x-1.5=5 $$

Solve the inequality. Write the solution in interval notation. $$|0.5 x-0.75|<2$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. \(x-y=7\)

Ice Deposits \(A\) roof has a 0.5 -inch layer of ice on it from a previous storm. Another ice storm begins to deposit ice at a rate of 0.25 inch per hour. (a) Find a formula for a linear function \(f\) that models the thickness of the ice on the roof \(x\) hours after the second ice storm started. (b) How thick is the ice after 2.5 hours?

Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. $$ \sqrt{5}(x-1.2)-\sqrt{3} x<5(x+1.1) $$

Solve the linear equation with the intersection-of-graphs method. Approximate the solution to the nearest thousandth whenever appropriate. $$ 8-2 x=1.6 $$