8
Review: equations and inequalities
Textbook: Part 1, lesson 8, pp. 25–27
GoalReview solving equations and inequalities and finding an unknown part.
New words
equation · tenglamaunknown · noma’lumroot (solution) · ildizinequality · tengsizlik
Explanation
A number that turns an equation into a true equality is its root. First simplify the left side: x + 172 + 28 = x + 200. Then find the unknown part by the rule and check by substituting. A solution of an inequality is any number that makes it true. For example, the natural solutions of m + 5 < 12 are 1, 2, 3, 4, 5, 6.
Worked examples
x + 172 + 28 = 500 → x + 200 = 500 → x = 500 − 200 = 300. Check: 300 + 172 + 28 = 500.
m + 5 < 12 → m < 7. There are 6 natural solutions: 1, 2, 3, 4, 5, 6.
Class activity
“Find the root”: the teacher writes an equation; children test the numbers on their cards by substituting and decide which one is the root.
Practice
1
Solve x − 53 = 29.
82
2
Solve 420 : m = 6.
70
3
Which of 3, 8, 12 is a root of 5 × x − 7 = 33?
8
4
How many natural solutions does y + 6 < 11 have?
4