A1: Solving Equations & Inequalities (Unit 1 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 + 25x + 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: −1/2x + 6 = −3/8 - 21/8x)

x = - 3

500

Solve: 2/5r − 4/5 = −4/25

r = 8/5

Inequalities

100

Solve and graph the inequality: 0 > 3x − 3 − 6

x < 3

200

Solve and graph the inequality: −6 > 5n + 5 + 4

n < -3

300

Solve and graph the inequality: 7 < −(−k − 3) + 2

k > 2

400

Solve and graph the inequality: −5(1 − 4a) > −5

a > 0

500

Solve and graph the inequality: 2 − 9r < −2(r + 3) − 4

r > 2

Compound Inequalities

100

Solve and graph the following inequality: x - 6 ≤ -11 or (x/3)>-1

x ≤ -5 or x > -3

200

Solve and graph the following inequality: -19 < 5 - 3x < 11

-2 < x < 8

300

Solve and graph the following inequality: 2b + 17 > 17 or 4b + 2 ≤ -14

b > 5 or b ≤ -4

400

Solve and graph the following inequality: -4n - 3 < -19 and 7n - 11/5 ≤ 31

4 < n ≤ 6

500

Solve and graph the following inequality: 7 ≥ 3r + 1 > -14

-5 < r ≤ 2

Application

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. Write an equation to show how many miles Ann drove.

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. Write an equation that represents the number of questions that were on Tim's math test.

4(x - 10) = 76

300

WRITE AN EQUATION for the following situation. Assume x represents the width. The width of a rectangle is 6 inches more than the length. The perimeter of the rectangle is 24 inches. What is the length and width of the rectangle? Write a SIMPLIFIED equation that could be used to answer this question.

4x + 12 = 24

400

WRITE AN EQUATION for the following situation. Assume x represents the first number. The sum of 3 consecutive odd numbers is 45. What are the numbers? I DON'T WANT THE SOLUTIONS!  I WANT AN EQUATION!!!

3x + 6 = 45

500

Write AND solve an equation for the following situation. On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game bowled is $3.50. On Sunday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. Let x equal the number of games bowled.  If you spent the same amount each day, how many TOTAL games were bowled over the weekend?

3.5x + 2 = 3.25x + 5; 12 games were bowled.