Chapter 2 - Linear Equations

Simple Equations

100

Translate into an equation:

One half of m cubed in the same as four times m minus nine

1/2m³ = 4m - 9

200

Solve:

2/5b = -4

b = -10

300

Max is four years younger than his sister Brenda. Max is 16 years old. Write and solve an equation to find Brenda's age.

x - 4 = 16

x = 20 years old 

400

Solve for n:

n/4 - 7 = -2

n = 20

500

Find three consecutive integers with a sum of -39

-12, -13, -14

Multi-step Equations

100

Solve:

5y - 4 = 9y + 18

y = -3

200

Solve:

3(-2k - 2) = -2(3k - 11)

no solution

300

Abby started a savings account with $100 and she saves at a rate of $40 a month. Jim started a savings account with $160 and he saves at a rate of $25 a month. Write and solve an equation to find out how long until Abby and Jim have the same amount of money in their accounts.   

100 + 40x = 150 + 25x

x = 4 months

400

Rectangle A has side lengths of x and (x+3). Rectangle B has side lengths of 14 and (x - 4). Write and solve an equation to find the value of x so that both rectangles have the same perimeter.

2(x) + 2(x + 3) = 2(14) + 2(x - 4)

x = 7

500

Find the smallest odd integer if the sum of the first two consecutive odd integers is equal to twenty-four less than four times the third consecutive odd integer.

x + x + 2 = 4(x + 4) - 24

x = 5

Absolute Value Equations

100

Evaluate the absolute value expression if m = -8, n = 4, and p = -12:

-3 l 6n - 2p l

-144

200

Evaluate the absolute value expression if m = -8, n = 4, and p = -12:

4 l 7m + 3p l + 4n

384

300

Solve the absolute value equation:

l -4w + 2 l = 14

-3 and 4

400

Solve the absolute value equation:

l 1/3d - 6 l = 15

-27 and 63

500

Draw a number line from -6 to 4.

Plot dots at -6 and 4. 

Find the absolute value equation for your picture.

l x + 1 l = 5

Ratios and Proportions

100

Does the ratio 18/32 form a proportion with the ratio 3/4?

no

200

Solve. Round to the nearest hundredth if necessary.

3/8 = 22/b

b = 58.67

300

Solve the proportion:

9/(k + 3) = 3/5

k = 12

400

A new gym is being built at the Greenfield Middle School. The length of the gym as shown on the builders blueprints is 12 inches. If the scale of the blueprint is 3/4 in = 5 ft, find the actual length of the new gym. 

80 feet

500

Ms. Garcia saw 8 commercials during a 24 minute program. At that rate, how many commercials would she see in a program that lasts an hour and a half?

30 commercials

Literal Analysis

100

Solve the equation 3x + 2y = 9 for y

y = (9-3x)/2

200

Solve 5x - 3y = 9 for y

y = 5/3x - 3

300

Solve A = 1/2bh for h

h = (2A)/b

400

The formula d = rt represents the distance "d" that an object moving at speed "r" travels in time "t". Solve the equation for "r". Then, find the average speed of a car that travels 240 miles in 5 hours.

r = d/t

r = 48 mph

500

The formula C = 6p + 200 gives C, the total cost in dollar of hosting a birthday party for "p" guests at a local ice cream parlor. Solve the formula for "p" and find out how many people can be invited to a party if the budget is $350.

p = (C - 200)/6

25 guests max