Solving Linear Equations

What you’ll learn

Keep both sides balanced while isolating an unknown.

រកអថេរដោយធ្វើប្រមាណវិធីដូចគ្នាទាំងពីរខាង។

Meaning and use

A linear equation in one unknown can often be arranged as ax + b = c. Apply the same valid operation to both sides to preserve equality. Divide by a only if it is nonzero. Substitute the result into the original equation to check it.

សមីការដឺក្រេទីមួយអាចសរសេរ ax+b=c។ ត្រូវធ្វើប្រមាណវិធីដូចគ្នាទាំងពីរខាង ហើយពិនិត្យចម្លើយក្នុងសមីការដើម។

Formulas

Solve when a is nonzero

\[ax+b=c\quad\Longrightarrow\quad x=\frac{c-b}{a}\]

Balance principle

\[u=v\quad\Longrightarrow\quad u+k=v+k\]

Symbols and units

Symbol	Meaning	Unit or restriction
x	Unknown value	Context-dependent
a	Coefficient of x	Nonzero in the displayed solution
b, c	Constant terms	Compatible units

Conditions and limits

• Division by zero is never a valid balancing step.
• If a = 0, inspect whether the remaining statement is true or false instead.
• ពិនិត្យដោយដាក់ចម្លើយត្រឡប់ក្នុងសមីការដើម។

Worked examples

One positive coefficient

Solve \(3x+5=20\).

1. Subtract 5: \(3x=15\).
2. Divide by 3: \(x=5\).
3. Check \(3(5)+5=20\).

x = 5

រក្សាតុល្យភាពសមីការដោយដក និងចែកទាំងពីរខាង។

A negative coefficient

Solve \(-2x+4=10\).

1. Subtract 4: \(-2x=6\).
2. Divide by −2: \(x=-3\).

x = −3

ចែកចំនួនវិជ្ជមាននឹងអវិជ្ជមាន បានចម្លើយអវិជ្ជមាន។

Common mistakes

Instead of	Use	Why
3x + 5 = 20 implies 3x = 25.	3x = 15.	Subtract 5 from both sides.
2x = 8 implies x = 6.	x = 4.	Undo multiplication by dividing, not subtracting.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Solve 2x + 3 = 11.
2. Solve 5x − 4 = 16.
3. Check x = 3 in 4x + 2 = 14.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. x = 4

   Subtract 3 to get 2x = 8, then divide by 2.

2. x = 4

   Add 4 to get 5x = 20, then divide by 5.

3. It is correct.

   4 × 3 + 2 = 14.

Quick recap

• Perform the same operation on both sides.
• Divide only by nonzero quantities.
• Check in the original equation.