104
Solving inequalities on the number ray
Textbook: Part 3, lesson 104, pp. 109–111
GoalShowing the solutions of inequalities on the number ray: x < 5, y ≥ 8.
New words
solution · yechimless than or equal · kichik yoki tengmarking · belgilashnumber ray · sonli nur
Explanation
To see all solutions of an inequality we mark them on the number ray. For x < 5 (“x is less than five”) we mark the numbers left of 5: among natural numbers 1; 2; 3; 4. The number 5 itself is not a solution; we show it as an empty circle. For y ≥ 8 (“y is greater than or equal to eight”) the number 8 and all numbers to its right are solutions: 8; 9; 10; … We mark 8 with a filled dot and continue to the right. The sign tells the side: “<” means left, “>” means right.
Worked examples
x < 5: a ray from 0 to 8; points 1, 2, 3, 4 are filled and 5 is an empty circle. There are 4 solutions.
If the right side is an expression we calculate it first: x < 20 × 3 − 45 = 15, i.e. x < 15. The largest natural solution is 14.
Class activity
“Step on the ray”: a ray from 0 to 10 is drawn on the floor. The teacher names an inequality (z < 6) and the children standing on solution numbers step forward.
Practice
1
How many natural solutions does x < 5 have?
4
2
How many natural solutions does z ≤ 6 have?
6
3
Among the numbers from 5 to 12, for how many is y ≥ 8 true?
5
4
Dilnoza read 8 pages in an hour, Jasur read fewer. At most how many pages could Jasur have read?
7
5
Find the largest natural solution of x < 20 × 3 − 45.
14