Chapter 7

Solve. $$3 x+2-17 x-2=-48 \times 2-4$$

Barry drove the 24 miles to town and then back in 1 hour. On the return trip, he was able to average 14 miles per hour faster than he averaged on the trip to town. What was his average speed on the trip to town?

Simplify. $$ 1 x+2-1 x-3 $$

Simplify. (Assume all denominators are nonzero.) $$ 1 a b+21 a+1 b $$

Construct a mathematical model given the following. \(y\) varies directly as the square of \(x,\) where \(y=3\) when \(x=1 / 2\)

Solve. $$x-1+3=0$$

Jerry paddled his kayak upstream against a 1-mile-per-hour current for 12 miles. The return trip downstream with the 1 -mile-per-hour current took 1 hour less time. How fast can Jerry paddle the kayak in still water?

Simplify. $$ x x+1-2 x-2 $$

Simplify. (Assume all denominators are nonzero.) $$ 1 y+1 x x y $$

Construct a mathematical model given the following. \(y\) is inversely proportional to the square of \(x\), where \(y=27\) when \(x=\) \(1 / 3 .\)

State the restrictions to the domain. $$ 12 x(x+3)(2 x-1) $$

Given \(f(x)=16 \times 2-9 x+5\) and \(g(x)=x 2+3 x-104 x 2+5 x-6,\) calculate \((f \cdot g)(x)\) and state the restrictions.

Divide. (Assume all denominators are nonzero.) $$ (x-4) 230 x 4 \div x-415 x $$

Solve. $$4-y-1=0$$

It takes a light aircraft 1 hour more time to fly 360 miles against a 30 - mile-per-hour headwind than it does to fly the same distance with it. What is the speed of the aircraft in calm air?

Simplify. $$ 2 x-3 x+5-x x-3 $$

Simplify. (Assume all denominators are nonzero.) $$ 3 x 13-1 x $$

Construct a mathematical model given the following. \(y\) is inversely proportional to the square of \(x\), where \(y=9\) when \(x=\) \(2 / 3\)

State the restrictions to the domain. $$ x-3(3 x-1)(2 x+3) $$

Divide. (Assume all denominators are nonzero.) $$ 5 y 410(3 y-5) 2 \div 10 y 52(3 y-5) 3 $$

Solve. $$y-2-4=0$$

James can paint the office by himself in 7 hours. Manny paints the office in 10 hours. How long will it take them to paint the office working together?

Simplify. (Assume all denominators are nonzero.) $$ 1-4 x-21 x 21-2 x-15 x 2 $$

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and the square of \(z\), where \(y=54\) when \(x=2\) and \(z=3\)

Simplify. (Assume all denominators are nonzero.) $$ 5 x y-3 y $$

Solve. $$9 x-2-1=0$$

Barry can lay a brick driveway by himself in 12 hours. Robert does the same job in 10 hours. How long will it take them to lay the brick driveway working together?

Simplify. $$ 3 y-13 y-y+4 y-2 $$

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and the square of \(z,\) where \(y=6\) when \(x=1 / 4\) and \(z=2 / 3\)

Simplify. (Assume all denominators are nonzero.) $$ x x 2-x-6-3 x 2-x-6 $$

Solve. $$3(x-1)-1+5=0$$

Jerry can detail a car by himself in 50 minutes. Sally does the same job in 1 hour. How long will it take them to detail a car working together?

Simplify. $$ 2 x-52 x+5-2 x+52 x-5 $$

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and \(z\) and inversely as the square of \(w,\) where \(y=\) 30 when \(x=8, z=3,\) and \(w=2\)

Solve. $$5-2(3 x+1)-1=0$$

Jose can build a small shed by himself in 26 hours. Alex builds the same small shed in 2 days. How long would it take them to build the shed working together?

Simplify. $$ 22 x-1-2 x+11-2 x $$

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and \(z\) and inversely as the square of \(w,\) where \(y=5\) when \(x=1, z=3,\) and \(w=1 / 2\).

State the restrictions and then simplify. \(12 x 660 x\)

Simplify. (Assume all denominators are nonzero.) $$ 3 x-7+1-2 x x 2 $$

Divide. (Assume all denominators are nonzero.) $$ 24 a 2 b 3(a-2 b) \div 12 a b(a-2 b) 5 $$

Solve. $$3+2 x-3=2 x-3$$

Allison can complete a sales route by herself in 6 hours. Working with an associate, she completes the route in 4 hours. How long would it take her associate to complete the route by herself?

Simplify. $$ 3 x+4 x-8-28-x $$

Construct a mathematical model given the following. \(y\) varies directly as the square root of \(x\) and inversely as \(z\), where \(y=\) 12 when \(x=9\) and \(z=5\)

Simplify. (Assume all denominators are nonzero.) $$ 7 x 4 x 2-9 x+2-2 x-2 $$

James can prepare and paint a house by himself in 5 days. Working with his brother, Bryan, they can do it in 3 days. How long would it take Bryan to prepare and paint the house by himself?

Simplify. $$ 1 y-1+11-y $$

Construct a mathematical model given the following. \(y\) varies directly as the square root of \(x\) and inversely as the square of \(z,\) where \(y=15\) when \(x=25\) and \(z=2\).

State the restrictions and then simplify. $$ 20(x-3)(x-5) 6(x-3)(x+1) $$