Algebra: Solving Equations & Inequalities (Unit 3 Review)

Multistep Equations

100

Solve: −18 − 6k = 6(1 + 3k)

k = -1

200

Solve: 2(4x − 3) − 8 = 4 + 2x

x = 3

300

Solve: 24a − 22 = −4(1 − 6a)

No solution

400

Solve: −5(1 − 5x) + 5(−8x − 2) = −4x − 8x

x = -5

500

Solve: 10p + 9 − 11 − p = −2(2p + 4) − 3(2p − 2)

p = 0

Equations and Fractions

100

Solve: 4/3 n − 2/3 n = 4/3

n = 2

200

Solve: 2.4 = 0.6(−x − 3)

x = -7

300

−1.6 + 1/2 n = −0.7(−6 + 8n) + 0.3

n = 1

400

Solve: −1/2 (x − 12) = −3/8 (1 + 7x)

x = - 3

500

Solve: −0.3(2/5r − 4/5) = −4/25

r = 10/3

Application 1

100

Write a simplified equation for the following situation. The length of a rectangle is 4 times its width. The perimeter is 40. Use x to represent the width of the rectangle. What are the dimensions of the rectangle?

10x = 40

200

Write a simplified equation for the following situation. The length of a rectangle is 4 more than half the width. The perimeter of the rectangle is 68. Assume x represents the width of the rectangle. Find the length and width of the rectangle.

3x + 8 = 68

300

Write a simplified equation for the following situation. Find 3 consecutive even integers whose sum is 348.

3x + 6 = 348

400

Write an UNsimplified equation for the following situation. An apple has 24 fewer calories than a banana. If 7 bananas have the same number of calories as 10 apples, how many calories are in a banana? Assume x represents the number of calories in a banana.

7x = 10(x - 24)

500

Write AND solve an equation for the following situation. I have $2.85 in quarters and nickels. In nickels, I have 2 more than half the amount of quarters. Assume q represents quarters. How many of each coin do I have?

.25q + .05(1/2q + 2) = 2.85

10 quarters

7 nickels

Compound Inequalities

100

x - 6 ≤ -11 or (x/3)>-1

x ≤ -5 or x > -3

200

-19 < 5 - 3x < 11

-2 < x < 8

300

2b + 7 > 17 or 4b + 2 ≤ -14

b > 5 or b ≤ -4

400

-4n - 3/2 < -20 and 7/10n - 11/5 ≤ 2

37/8 < n ≤ 6

500

7/4 ≥ 3/2r - 1/2 > -6

-11/3 < r ≤ 3/2

Application 2

100

Write an equation for the following situation. Assume x represents the number of miles driven. Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5. Ann paid a total of $49.10. How many miles did Ann drive?

2.1x + 5 = 49.1

200

Write an equation for the following situation. Assume x represents the number of questions on the test. Tim answered all the questions on his math test but got 10 answers wrong. He received 4 points for every correct answer, and there was no penalty for wrong answers. His score was 76 points. How many questions were on Tim's math test?

4(x - 10) = 76

300

Write an equation for the following situation. Assume x represents the time that Train A has traveled in hours. At 10:00 AM train A left the station and an hour later train B left the same station on a parallel track. If train A traveled at a constant speed of 60 miles per hour and train B at 80 miles per hour, after how many hours did train B pass train A?

60x = 80(x - 1)

400

Write a simplified equation for the following situation. The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side (x) if the perimeter is 45?

3x - 6 = 45

500

Write AND solve an equation for the following situation. Suppose Ken has coins in nickels and dimes only and has a total of $1.60. If x represents the number of dimes, and he has twice as many nickels as dimes, how many of each coin does he have?

.1x + .05(2x) = 1.60

He has 8 dimes and 16 nickels.