Linear Equations & Inequalities

Equations

100

Solve for x. 

(2/3)x = 36

x = 54

200

Solve for x. 

-2x - 10x + 12 = 18

x = -1/2

300

Solve. 

4(x - 3) = 2x - 8

x = 2

400

Solve.

12(x + 6) = 8(x - 6) + 4x + 120

All real numbers

500

Solve for b. 

8a - 4b = 36

b = 2a - 9

Inequalities

100

Solve for x. 

3 - 2x > 11

x < -4

200

To advance to the next level of a competition, Rachel must earn at least 180 points. She has already earned 145 points. Write and solve an inequality to find the number of points p she needs to advance to the next level of the competition.

145 + p > 180 p > 35 points

300

Solve. 

4 < -2x + 3 < 9

-1/2 x > x > -3 (or -3 < x < -1/2)

400

Solve. 

-12 < 2x + 8 < 18

-10 < x < 5

500

Solve 

2(5x - 1) < 7 + 10x

-2 < 7 --> All real numbers

Absolute Value Equations

100

Solve. 

|2x - 9| = 15

x = -3 and x = 12

200

Solve 

|x + 6| = 2x

x = 6, -2

300

Solve 

|x - 1| + 5 = 2

No solution

or 

x = -2, 4

400

Solve 

|5x - 4| = 16

x = 4, -12/5

500

Write an absolute value equation that has the given solutions: 3 and 9.

|x - 6| = 3

Absolute Value Inequalities

100

Solve 

|8x - 11| < -1

No solution

200

Solve 

|x + 2| - 3 > 6

x>7 OR x<-11

300

Solve 

3|x + 1| - 7 > -1

x < -3 or x > 1

400

Solve 

6|-x + 3| + 7 > 7

x < 3 or x > 3

500

Solve 

2|2x - 3| - 4 > 6

x < -1 or x > 4

Misc.

100

What are the order of operations?

GEMDAS

200

What day of the year is Pi Day Celebrated on?

3/14

300

The founder of The Pythagorean Theorem

Who is Pythagoras

400

Little Timmy is 7 years old. In 5 years his Aunt will be 3 times older than him. How old is she now?

31 years old

500

Three consecutive odd integers sum to 153. What is the largest of the integers?

53