Algebra: Solving Equations & Inequalities

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 = 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(1 − 4r) < −2(r + 3) − 4

r > 2

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 + 17 > 17 or 4b + 2 ≤ -14

b > 5 or b ≤ -4

400

-4n - (3/2) < -20 and (7/10)n - (11/5) ≤ 2

(37/8) < n ≤ 6

500

(7/4) ≥ (3/2)r - (1/2) > -6

(-11/3) < r ≤ (3/2)

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. 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. On Friday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game bowled is $3.50. On Saturday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. If you spent the same amount each day, how many games, x, were bowled?

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