Equations and Inequalities

Equations with brackets, fractions and unknowns on both sides — then inequalities, which behave identically except for the one rule that reverses everything.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ต่อยอดจาก ม.1 บทที่ 6 สมการเชิงเส้น ไปยัง ม.3 บทที่ 1 อสมการ
Common Core (US): 7.EE, A-REI
Cambridge: Lower Secondary Stage 8 — Algebra: expressions, equations and formulae

5.1 Equations with brackets and unknowns on both sides

The order that always works

1Clear any fractions by multiplying every term by the common denominator
2Expand the brackets
3Collect the letter terms on one side and the numbers on the other
4Divide to finish
5Substitute the answer back into the original equation

ตัวอย่าง 1

Solve $4 (x - 3) = 2 (x + 5)$

วิธีทำ

1.Expand both sides: $4 x - 12 = 2 x + 10$
2.Subtract $2 x$ : $2 x - 12 = 10$
3.Add $12$ : $2 x = 22$
4.Check: $4 (11 - 3) = 32$ and $2 (11 + 5) = 32$

ตอบ $x = 11$

ตัวอย่าง 2

Solve $\frac{x}{3} + \frac{x}{4} = 14$

วิธีทำ

1.Common denominator $12$ — multiply every term by $12$
2. $4 x + 3 x = 168$
3. $7 x = 168$

ตอบ $x = 24$

ข้อควรระวัง

When you multiply through to clear fractions, every term is multiplied — including the one on the right that has no fraction in it. Missing it is the reason an otherwise correct solution comes out wrong.

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