6th Grade Inequalities on the Number Line Worksheet Solutions (PDF)
This grade 6 inequalities answers for 6th Grade covers inequalities on the number line (Common Core 6.EE.B.5, 6.EE.B.8), with a free PDF to print.
Grade 6 · Common Core State Standards: 6.EE.B.5, 6.EE.B.8
Grade 6 inequalities answers: exercises 1 to 10
Exercise 1 – Is it a solution? (greater than)
\(6 > 4\) is true.
Yes.
Exercise 2 – Is it a solution? (at least)
\(4 \ge 9\) is false because 4 is less than 9.
No.
Exercise 3 – Is it a solution? (expression)
Substitute: \(8 + 2 = 10\), and \(10 < 10\) is false.
No. 8 is not a solution.
Exercise 4 – Graph x > 3
Draw an open circle at 3 because 3 is not included, and shade to the right.
See the graph.
Exercise 5 – Graph x <= 2
Draw a closed circle at 2 because 2 is included, and shade to the left.
See the graph.
Exercise 6 – Graph with a negative
Closed circle at \(-1\), shade to the right.
See the graph.
Exercise 7 – Write from a graph (open)
The circle is open at 4 and the ray goes right.
\(x > 4\)
Exercise 8 – Write from a graph (closed)
The circle is closed at \(-2\) and the ray goes left.
\(x \le -2\)
Exercise 9 – Less than
\(x < 7\)
Exercise 10 – At least
“At least” means 12 or more.
\(x \ge 12\)
Exercises 11 and up
Exercise 11 – No more than
“No more than” means 20 or less.
\(x \le 20\)
Exercise 12 – More than
\(x > 15\)
Exercise 13 – List solutions
Any number greater than 5 works, such as 6, 7.5, and 100.
For example: 6, 7.5, 100
Exercise 14 – Solutions with decimals
Sample solutions: 2.5, 3, 10.
Yes, 2.5 is a solution because \(2.5 \ge 2.5\) is true.
2.5, 3, 10; yes
Exercise 15 – Speed limit
Legal speeds are 65 or less: \(s \le 65\). (Speeds are also at least 0.)
\(s \le 65\)
Exercise 16 – Elevator
\(w \le 1500\).
\(1380 \le 1500\) is true.
\(w \le 1500\); yes, the group can ride
Exercise 17 – Game points
\(p \ge 8\). Closed circle at 8 and shade right.
\(p \ge 8\)
Exercise 18 – Book budget
\(4 \cdot 6 = 24 \le 25\): true.
\(4 \cdot 7 = 28 \le 25\): false.
He can buy at most 6 books.
Exercise 19 – Ride height
\(h > 48\).
\(48 > 48\) is false, and \(48.5 > 48\) is true.
\(h > 48\); 48 is not a solution, 48.5 is
Exercise 20 – Infinitely many
Every number greater than 3 is a solution: 3.1, 3.01, 3.001, and so on, as well as 4, 5, 100.
There is no greatest solution and always another number between 3 and any solution.
Infinitely many solutions
Exercise 21 – Snow day
\(t < 32\). Open circle at 32, shade left.
32 is not a solution; 31.5 is.
\(t < 32\)
Key facts behind this grade 6 inequalities answers
- An inequality uses <, >, ≤, or ≥ and usually has infinitely many solutions.
- Open circle: the number is not included (< or >).
- Closed circle: the number is included (≤ or ≥).
- Shade right for greater values and left for lesser values.
- At least means ≥ and at most or no more than means ≤.
How to use this grade 6 inequalities answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
Download the grade 6 inequalities answers as a PDF with the button below and keep it with your notes.
All Grade 6 chapters: Grade 6 math.
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