GoalConsolidate knowledge of equations and word problems from Chapter II.
New words
root · ildizsetting up an equation · tenglama tuzishno roots · ildizi yo‘qinfinitely many roots · cheksiz ko‘p ildiz
Explanation
In Chapter II we learned the notions of equation, root and linear equation, the two basic properties of equations and the solving procedure based on them. In equations with brackets and fractions we first open brackets and clear fractions by multiplying by a common denominator. If an equation reduces to 0 · x = b (b ≠ 0) it has no root; if it reduces to 0 · x = 0 it has infinitely many roots. In word problems we choose the unknown, set up an equation and solve it. In work, motion and age problems it is important to write the relations between quantities precisely. Always compare the answer with the condition.
A pupil read a 150-page book in 3 days. On the second day he read 30 pages more than on the first, and on the third day twice as many as on the first. If the first day was x pages: x + (x + 30) + 2x = 150, 4x = 120, x = 30 pages.
Class activity
“Equation relay”: team members take turns doing one step of an equation (open, move, combine, divide). The fastest team without errors wins.
Practice
1
Is 2 a root of 3x - 1 = 5?
Yes: 3 · 2 - 1 = 5.
2
Solve 3(2x - 1) - 2(x + 4) = 5.
x = 4
3
The sum of two numbers is 64 and one is 3 times the other. Find the smaller number.
16
4
Why do some equations have no root? Give an example.
After simplifying we may get a false equality; for example x + 1 = x + 2 leads to 1 = 2.