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 < (1/2)(4x + 16) < 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 - 2)/2| = 6.5

x = 3, -11/5

500

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

|x - 6| = 3

Absolute Value Inequalities

100

Solve |8x - 11| < 0

No solution

200

Solve |x + 2| - 3 > -6

All real numbers

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?

PEMDAS

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