2-1 SOLVING ONE-STEP EQUATIONS

Example 1. Solve each equation using addition or subtraction. Check your answer.

a. x – 10 = 4 a. x + 7 = 9

Example 2. Solve each equation using multiplication or division. Check your answer.

a. 7x = 56 b. 14 = -2w

c. d.

Example 3. Solve each equation. Check your answer.

a. b.

Example 4

One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this information find your maximum heart rate.


2-2 Solving Two-Step Equations

Example 1. Solve each equation. Check your answer.

a. / 7n + 12 = –23 / b. /

Example 2. A pizza shop charges $9 for a large cheese pizza. Additional toppings cost $1.25 per topping. Heather paid $15.25 for her large pizza. How many toppings did she order?

Example 3. Solve each equation. Check your answer.

a. / / b. /

Example 4. An online movie club offers a membership for $5 per month. Members can rent movies for $1.50 per rental. A member was billed $15.50 one month. Write and solve an equation to find how many movies the member rented.


2-3 Solving Multi-Step Equations

Example 1. Solve each equation. Check your answer.

a. 5n – 16 – 8n = –10 b. –34 = v + 42 – 5v

c. x – 1 + 5x = 23

Example 2. Five times a number decreased by 18 minus 4 times the same number is –36. What is the number?

Example 3. Solve each equation. Check your answer.

a. 42 = 3(2 – 3h) b. –10 = 5(2w – 4)

2-4 Solving Equations with Variables on both Sides

Example 1. Solve each equation. Check your answer.

a. –q – 11 = 2q + 4 b. 4t + 9 = –8t – 13

c. 22p + 11 = 4p – 7

Example 2. Tracey is looking at two different travel agencies to plan her vacation. ABC Travel offers a plane ticket for $295 and a rental car for $39 per day. M & N Travel offers a plane ticket for $350 and a rental car for $33 per day. What is the minimum number of days that Shirley’s vacation should be for M & N Travel to have the better deal?

Example 3. Solve each equation. Check your answer.

a. 2(2f – 4) = 2(f + 2) b. 3w – 6 + 2w = –2 + w


3-7 Absolute Value Equations and Inequalities

Example 1. Solve each equation.

a. |n| + 2 = 5 b. 4 = |s| - 3

Example 2. Solve each equation. If there is no solution, write no solution.

a. 1 = |g + 3| b. 3|d - 4| = 12

*Example 3*. Solve and graph each inequality.

a. |x| < 2 b. |y + 4| 12


2-6 Ratios, Rates, & Conversions

Example 1. Convert the given amount to the given unit.

a. 5 hr; min b. 6 days; hrs

Example 2. Car 1 drove 408 miles in 6 hours and Car 2 drove 365 miles in 5 hours during the cross-country road race. Who had the fastest average speed?

Example 3. Copy and complete each statement.

a. 8 dollars/hr = ___ cents/min

b. 10 mi/hr = ___ ft/min

Example 4. Find each unit rate.

4 pounds of green peppers cost $7.56.


2-7 Solving Proportions

Example 1. Solve each proportion using the Cross Product Property of Equality.

a. b. c.

Example 2. Eric is planning to bake approximately 305 cookies. If 3 pounds of cookie dough make 96 cookies, how many pounds of cookie dough should he make?

Example 3. Solve each proportion

a. b.


2-9 Percents

Example 1. Find each percent.

a. What percent of 150 is 350? b. What percent of 99 is 72?

Example 2. Find.

a. What is 125% of 62? b. What is 50% of 821?

Example 3. A used car lot runs sales at the end of the year to reduce inventory. This year the sale price is 15% less than the regular price. If the regular price of a car is $12,000, what is the sale price of the car?

Example 4. Find.

a. 15% of what number is 6.75? b. 5% of what number is 4.1?

Example 5. If you deposit $800 in a savings account that earns simple interest at a rate of 1.5% per year, how much interest will you have earned after 5 years?


2-10 Change Expressed as a Percent

Example 1. Tell whether each percent change is an increase or decrease. Then find the percent change. Round to the nearest percent.

a. Original amount: 23 b. Original amount: 83 c. Original amount: 19

New amount: 25 New amount: 41 New amount: 30

Example 2. The price of the truck was advertised as $19,900. After talking with the salesperson, Jack agreed to pay $18,200 for the truck. What is the percent decrease to the nearest percent?

Example 3. Find the percent error in each estimation. Round to the nearest percent.

You estimate the salesman is 45 years old. He is actually 38 years old.