Sketchy Skeletons (Writing & Graphing Inequalities)
Write an inequality: A number x is at least 7.
x >= 7
x+6 < 10
x < 4
3x+4 <= 19
x <= 5
Does x=0 satisfy x<-2 OR x>=3 ? Explain.
No; it satisfies neither condition.
|x| <= 4
-4 <= x <= 4
Describe the graph of x<-3.
Open circle at -3; shade left
x - 8 >= -3
x >= 5
2(x-3) > 8
x >7
-4 < x+1 <= 6
-5 < x <= 5
|x| > 3
x < -3 OR x > 3
A graph has a closed circle at 4 and shading to the left. Write the inequality. Is 4 included?
x <= 4; yes
x/4 <= -2
x <= -8
5x+8 > 4x-3
x > -11
2x < -6 OR x+2 >= 7
x< -3 OR x>= 5
|x+2| >= 5
x <= -7 OR x >=3
A Halloween party must have more than 10 guests but no more than 20. Write a compound inequality.
10 < g <= 20
-3x > 15
x < -5
3(x+2) - 4 <= x+10
x <= 4
-3 < 2x+1 <=9
-2 < x <= 4
| 2x - 7 | < 5 Solve, graph, and write internal notation.
1 < x < 6
open circles at 1 and 6 with line in between them
(1,6)
A haunted-house attraction requires a height of at least 48 inches. A student writes h > 48. Correct it, describe the graph, and explain the mistake.
h >= 48; closed at 48, shade right. Exactly 48 is allowed.
A student solves -2x <= 8 and gets x <= -4. Correct the answer and check using x=0.
x >= -4. Dividing by a negative reverses the sign. Since 0 <= 8, zero must be included.
You have $65. Halloween decorations cost $17, and each costume-contest prize costs $6. Write and solve an inequality. What is the greatest number of prizes you can buy?
17+6p <= 65, so p <= 8. Maximum: 8 prizes.
-7 <= -2x+3 <5
-1 < x<= 5