Chapter 3

Solve the equation. $$r-(-2)=5$$

Solve the equation. \(3(8+b)=27\)

Solve the formula for the indicated variable. Show all your steps. Then evaluate the new formula by substituting the given values. Area of a triangle: \(A=\frac{1}{2} b h\) Solve for \(h\) Find the value of \(h\) when \(A=24\) and \(b=8\)

Find the unit rate. Round your answer to the nearest hundredth. 8 to 136

Round to the nearest tenth. $$ -75.1234 $$

Solve the equation. Check your solution in the original equation. $$ \frac{4}{5} t=0 $$

Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. $$ 6 y-3 y+6=5 y-4 $$

Solve the equation. $$-1=d-(-12)$$

Solve the equation. \(-4(x+6)=12\)

Match the percent problem with the equation that represents it. $$39=0.50 b$$

Solve the formula for the indicated variable. Show all your steps. Then evaluate the new formula by substituting the given values. Solve \(A=\ell w\) for \(\ell\) Find the value of \(\ell\) when \(A=112\) and \(w=7\)

Find the unit rate. Round your answer to the nearest hundredth. 60 to 100

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 2.2 x=15 $$

Solve the equation. Check your solution in the original equation. $$ -4(m+6)+2 m=3(m+2) $$

You are making pies to sell at a fundraiser. It costs \(\$ 3\) to make each pie, plus a one-time cost of \(\$ 20\) for a pastry blender and a rolling pin. You plan to sell the pies for \(\$ 5\) each. Which equation could you use to find the number of pies you need to sell to break even, or recover your costs? A. \(3 x=20+5 x\) B. \(3 x+20=5 x\) C. \(3 x-20=5 x\) D. \(20-5 x=3 x\)

CAR TRIP Suppose you drive 630 miles from St. Louis, Missouri, to Dallas, Texas, in 10.5 hours. Solve the equation \(630=r(10.5)\) for \(r\) to find your average speed.

Solve the equation. $$6-(-y)=3$$

Solve the equation. \(\frac{3}{4}(x+6)=12\)

Solve the percent problem. How much money is 35% of $750?

Solve the formula for the indicated variable. Show all your steps. Then evaluate the new formula by substituting the given values. Solve \(A=\frac{1}{2} b h\) for \(b\) Find the value of \(b\) when \(A=22\) and \(h=4\)

Find the unit rate. Round your answer to the nearest hundredth. $$\frac{6}{8}$$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 14-9 x=37 $$

You put some money in your pocket. You spend \(\$ 4.50\) on lunch. You have \(\$ 7.50\) in your pocket after buying lunch. Write an equation to find how much money you had before lunch.

STATING INVERSES State the inverse operation. Divide by 6

Solve the equation. \(\frac{1}{3}(x-1)=6\)

Solve the formula for the indicated variable. Show all your steps. Then evaluate the new formula by substituting the given values. The formula for the perimeter of a rectangle is \(P=2 \ell+2 w .\) Find the area of a rectangle that has perimeter \(P\) of 18 centimeters and length \(\ell\) of 6 centimeters. HINT: You can begin by solving the perimeter formula for \(w\).

Solve the percent problem. What number is 25% of 80?

Solve the equation. Check your solution in the original equation. $$ \frac{3}{8}(16 x-8)=9-5(x-2) $$

Find the unit rate. Round your answer to the nearest hundredth. $$\frac{66}{18}$$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 3(3 t-14)=-4 $$

Describe the first step you would use to solve the equation. $$ x+2=3 x-4 $$

You put some money in your pocket. You spend \(\$ 4.50\) on lunch. You have \(\$ 7.50\) in your pocket after buying lunch. Which inverse operation will you use to solve the equation?

STATING INVERSES State the inverse operation. Multiply by \(5 .\)

Solve the equation. \(\frac{2}{3}(x+8)=8\)

In Exercises 18 and \(19,\) use the formula for density. \(d=\frac{m}{v},\) where \(m=\) mass and \(v=\) volume. Find a formula for \(v\) in terms of \(d\) and \(m .\)

Solve the percent problem. What distance is 24% of 710 miles?

Solve the equation. Check your solution in the original equation. $$ \frac{1}{5}(25-5 k)=21-3(k-4) $$

Find the unit rate. Round your answer to the nearest hundredth. $$\frac{15}{20}$$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 2.69-3.64 x=23.78 x $$

Describe the first step you would use to solve the equation. $$ 5 t+12=2 t $$

You put some money in your pocket. You spend \(\$ 4.50\) on lunch. You have \(\$ 7.50\) in your pocket after buying lunch. Solve the equation. What does the solution mean?

STATING INVERSES State the inverse operation. Multiply by \(\frac{2}{3}\)

Solve the equation. \(48=11 n+26\)

In Exercises 18 and \(19,\) use the formula for density. \(d=\frac{m}{v},\) where \(m=\) mass and \(v=\) volume. Use the formula you wrote in Exercise 18 to find the volume of a piece of cork that has a density of 0.24 grams per cubic centimeter and a mass of 4.0 grams. Round to the nearest hundredth.

Solve the percent problem. 14% of 220 feet is what length?

Solve the equation. $$ 3(x+6)=5(x-4) $$

Find the unit rate. Round your answer to the nearest hundredth. $$\frac{28}{35}$$

You spend a total of $13.80 at a restaurant. This includes the price of dinner and a 15% tip. What is the price of dinner without the tip? Use a verbal model to solve the problem.

Describe the first step you would use to solve the equation. $$ 2 x-7=-8 x+13 $$

STATING INVERSES State the inverse operation. Multiply by \(-4\)