100
Equalities and inequalities
Textbook: Part 3, lesson 100, pp. 98–100
GoalTell apart an expression, an equality, an inequality and an equation; solutions of an inequality such as x < 7.
New words
equality · tenglikinequality · tengsizlikequation · tenglamaunknown · noma’lum
Explanation
An expression is a notation of numbers and operation signs: x + 21. An equality joins two expressions with “=”: 18 − 6 = 12; it can be true or false. An inequality joins two expressions with “<” or “>”: c < 8. An equation is an equality with an unknown number: 20 − k = 11. The inequality x < 7 is read “x is less than seven” and among natural numbers it is true for x = 1; 2; 3; 4; 5; 6. If it is x ≤ 7 (“less than or equal”), 7 is a solution too.
Worked examples
x + 12 is an expression; 5 × 4 = 20 is a true equality; 9 + 2 < 8 is a false inequality (11 > 8); 3 × y = 18 is an equation (y = 6).
The inequality a < 4 is true for the natural numbers a = 1; 2; 3: three solutions in all.
Class activity
“Sort the cards”: the teacher writes notations on cards (expression, equality, inequality, equation). Children place each card in the right group and say whether an equality or inequality is true or false.
Practice
1
For how many natural numbers is the inequality x < 6 true?
5
2
Put the correct sign (“<” or “>”) in 2 340 + 1 750 ... 4 000.
>
3
Which of these is an equation: x + 5 = 12, x + 5, 7 + 5 = 12?
x + 5 = 12
4
A rectangular hall has length a = 7 m and width b = 5 m. Find the value of a × 2 + b × 2 (the perimeter, m).
24
5
Is the product of 64 and 4 less than 250? Find the product.
256