40
Solving linear equations with one unknown and integer coefficients
Textbook, pp. 186–191
GoalSolve linear equations with one unknown and integer coefficients.
New words
equation · tenglamaunknown · noma’lumroot (solution) · ildiz (yechim)moving a term · hadni o‘tkazish
Explanation
Solving an equation means finding the value of the unknown that makes it a true equality. If we add the same number to both sides, or multiply or divide both sides by a nonzero number, the solution does not change. That is why we may move a term to the other side with a changed sign. The steps: remove brackets, collect unknown terms on one side and numbers on the other, combine like terms, divide by the coefficient and check the solution.
Worked examples
3x − 7 = 11: 3x = 11 + 7 = 18, x = 18 : 3 = 6. Check: 3 · 6 − 7 = 11.
5(x − 2) = 4x + 3: 5x − 10 = 4x + 3, 5x − 4x = 3 + 10, x = 13. Check: 5 · 11 = 55 and 4 · 13 + 3 = 55.
Class activity
“Balance equation”: a balance scale is drawn with the two sides of an equation. Pupils add or remove the same “weight” on both pans to keep it balanced and isolate x.
Practice
1
Solve 2x + 9 = 3.
-3
2
Solve 7x − 4 = 3x + 20.
6
3
Solve 3(x + 4) = 21.
3
4
Why does a term change sign when moved to the other side?
We subtract (or add) the same number on both sides: in x + 5 = 9, subtracting 5 from both sides gives x = 9 − 5.