Equations and Inequalities

Linear equations on both papers, then quadratic equations by every method the syllabus allows, simultaneous equations including the linear-and-quadratic case, and inequalities on a number line.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ครอบคลุม ม.3 บทที่ 1 อสมการ · บทที่ 3 สมการกำลังสอง · บทที่ 6 ระบบสมการ
Common Core (US): A-REI, 8.EE
Cambridge: IGCSE 0580 — Topic 2: Algebra and graphs (Core and Extended)

3.1 Linear equations

The only topic in this chapter that is on the Core paper as well as the Extended one, and the one every later method quietly assumes.

Whatever is done to one side is done to the other

1Multiply out any brackets
2Collect the $x$ terms on the side where the coefficient ends up positive
3Collect the numbers on the other side
4Divide by the coefficient of $x$ — and leave a fraction as a fraction unless asked

ตัวอย่าง 1

Solve $3 x + 4 = 10$ .

วิธีทำ

1. $3 x = 10 - 4 = 6$
2. $x = \frac{6}{3}$

ตอบ $x = 2$

ตัวอย่าง 2

Solve $5 - 2 x = 3 (x + 7)$ .

วิธีทำ

1.Expand the bracket: $5 - 2 x = 3 x + 21$
2.Move the $x$ terms to the right, where they stay positive: $5 = 5 x + 21$
3. $- 16 = 5 x$

ตอบ $x = - \frac{16}{5} = - 3.2$

เคล็ดลับ

Substitute your answer back into the ORIGINAL equation, not into a line of your own working. Checking $5 - 2 (- 3.2) = 11.4$ against $3 (- 3.2 + 7) = 11.4$ takes ten seconds and catches a sign slip that would otherwise travel all the way to the answer line.

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