Algebra 1 - Inequalities

Addition and Subtraction

100

x - 7 > 3

{x|x>10}

200

- 13 > w + 12

{w|w < -25}

300

The sum of two consecutive integers is at most 7. What is the largest possible value for the lesser integer?

3

400

The sum of two consecutive integers is at most 3. What is the greatest possible value for the greater integer?

2

500

You and your friend are planning to walk across an old bridge that can hold at most 1000 pounds. The total weight of the people currently on the bridge is 675 pounds. You weigh 156 pounds. Write and solve an inequality that represents how much your friend can weigh within the limits of the bridge.

x < 169

Multiplication and Division

100

t/-2 > 4

{t|t < -8}

200

-3.5z < 42

{z|z > -12}

300

Pete's grade on a test was within 5 points of his class average of 94. What is his range of grades on the test?

89 < or = g < or = 99

400

b/8 > -1/5

{b|b > -1 3/5}

500

-3m < -18

{m|m > 6}

Compound Inequalities

100

5t + 8 < or = 3t - 3

{t|t < or = -5.5}

200

1.9 + 1.7x < 2.1(3 + x)

{x|x > -11}

300

3(-w - 6) < 2(2w + 8) + 1

{w|w > -5}

400

Solve AND graph the solution set: w/3 < 1 OR 3w + 5 > 11

{w|w is a real number} Graph of a line showing all real numbers.

500

2 + 3x > 8 OR 4 - 7x < or = -17

{x|x > 2} open circle over 2 on the number line, arrow pointing to the right (increasing positive numbers)

Absolute Value

100

Graph the solution set: |x - 2| > or = 3

Filled in circle over -1, pointing to the left, filled in circle over 5, pointing to the right.

200

What is the solution set of |2x - 3| > 4?

{x|x < -0.5 or x > 3.5}

300

Solve and Graph: |2x - 5| < 3

{x|1< x < 4}

400

Solve and Graph: |z + 4| > or = 7

{z|z < or = -11 OR z > or = 3} filled in circle over -11, pointing left, filled in circle over 3, pointing right.

500

5|-p+2| + 4 > 4

All real numbers

Potpourri

100

Graph y < or = 3x

line, m = 3, goes through (0,0), right half is shaded.

200

Use a graph to solve 2y-4x < 8

dotted line, y = 2x + 4, y intercept is 4, x intercept is -2, shaded on right side.

300

graph the inequality 

5x-2y<10

b=-5, m=5/2, dotted line, shaded above or on the left side of the line

400

Which of the ordered pairs are a part of the solution of: y + 1 > 1/2x +3 f. (2, 3) g. (-4, 0) h. (1, 2) j (-3, 1)

j. (-3, 1)

500

Laurie and Maya sold at most $50 worth of get-well friendship cards. The friendship cards, x, were sold for $2 each and the get - well cards, y, were sold for $1.50 each. Which point represents a reasonable number of cards sold? f. (20, 10) g. (15, 10) h. (18, 20) j. (10, 30)

g. (15, 10)