a linear equation ∈ one variable is of the form ax + b = 0, where a ≠ 0
to solve for x, we use the formula x = -b/a
we can also represent linear equations ∈ the form x = c, where c is a constant
for example, 2x = 5 is a linear equation, which can be solved as x = 5/2
we can also have linear equations ∈ the form x/a = b, which can be solved as x = ab
for example, x/2 = 3 can be solved as x = 2 × 3 = 6
we can also represent linear equations ∈ the form ax = b, which can be solved as x = b/a
for example, 3x = 12 can be solved as x = 12/3 = 4
we can also have linear equations ∈ the form ax + b = c, which can be solved as x = (c - b)/a
for example, 2x + 3 = 7 can be solved as x = (7 - 3)/2 = 4/2 = 2

🪤 The 5 Mistakes That Cost Marks

not checking if the coefficient of x is zero before solving the equation
not using the correct formula to solve the equation
not simplifying the equation before solving for x
not checking the solution by plugging it back into the original equation
not writing the final answer ∈ the correct format, for example, x = 2 instead of x = 2.0

✏️ 3 Solved PYQs

Question 1: Solve the equation 2x + 5 = 11 step 1: subtract 5 from both sides, we get 2x = 11 - 5 = 6 step 2: divide both sides by 2, we get x = 6/2 = 3 therefore, the solution is x = 3
Question 2: Solve the equation x/4 = 9 step 1: multiply both sides by 4, we get x = 9 × 4 = 36 therefore, the solution is x = 36
Question 3: Solve the equation x - 3 = 7 step 1: add 3 to both sides, we get x = 7 + 3 = 10 therefore, the solution is x = 10

🧠 The One Thing Most Students Get Wrong

most students get wrong the concept of solving linear equations with variables on both sides
for example, the equation 2x + 3 = 5x - 2 can be solved by first adding 2 to both sides, we get 2x + 5 = 5x
then, subtract 2x from both sides, we get 5 = 3x
finally, divide both sides by 3, we get x = 5/3
therefore, the solution is x = 5/3

👁️ Ayush's Note

to solve linear equations, first simplify the equation by combining like terms
then, isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation
finally, check the solution by plugging it back into the original equation
for example, to solve the equation 2x + 2 = 6, first subtract 2 from both sides, we get 2x = 4
then, divide both sides by 2, we get x = 2
therefore, the solution is x = 2

🔁 Last 5 Minutes Box

∈ the last 5 minutes of the exam, quickly review the formulas and concepts of linear equations
make sure to check the solutions by plugging them back into the original equations
also, make sure to write the final answers ∈ the correct format
for example, x = 2 instead of x = 2.0
quickly review the steps to solve linear equations, such as adding, subtracting, multiplying, or dividing both sides of the equation

📝 Practice MCQs

1. Question: Solve the equation x + 2 = 9

A) x = 7

B) x = 11

C) x = 10

D) x = 8

Answer: A) x = 7, because subtracting 2 from both sides gives x = 9 - 2 = 7

2. Question: Solve the equation 2x = 12

A) x = 5

B) x = 6

C) x = 4

D) x = 8

Answer: B) x = 6, because dividing both sides by 2 gives x = 12/2 = 6

3. Question: Solve the equation x - 1 = 3

A) x = 2

B) x = 4

C) x = 5

D) x = 6

Answer: B) x = 4, because adding 1 to both sides gives x = 3 + 1 = 4

4. Question: Solve the equation x/3 = 2

A) x = 5

B) x = 6

C) x = 4

D) x = 8

Answer: B) x = 6, because multiplying both sides by 3 gives x = 2 × 3 = 6

5. Question: Solve the equation 2x + 1 = 7

A) x = 2

B) x = 3

C) x = 4

D) x = 5

Answer: B) x = 3, because subtracting 1 from both sides gives 2x = 6, then dividing both sides by 2 gives x = 6/2 = 3

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

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a linear equation ∈ one variable is of the form ax + b = 0, where a ≠ 0
to solve for x, we use the formula x = -b/a
we can also represent linear equations ∈ the form x = c, where c is a constant
for example, 2x = 5 is a linear equation, which can be solved as x = 5/2
we can also have linear equations ∈ the form x/a = b, which can be solved as x = ab
for example, x/2 = 3 can be solved as x = 2 × 3 = 6
we can also represent linear equations ∈ the form ax = b, which can be solved as x = b/a
for example, 3x = 12 can be solved as x = 12/3 = 4
we can also have linear equations ∈ the form ax + b = c, which can be solved as x = (c - b)/a
for example, 2x + 3 = 7 can be solved as x = (7 - 3)/2 = 4/2 = 2

🪤 The 5 Mistakes That Cost Marks

not checking if the coefficient of x is zero before solving the equation
not using the correct formula to solve the equation
not simplifying the equation before solving for x
not checking the solution by plugging it back into the original equation
not writing the final answer ∈ the correct format, for example, x = 2 instead of x = 2.0

✏️ 3 Solved PYQs

Question 1: Solve the equation 2x + 5 = 11 step 1: subtract 5 from both sides, we get 2x = 11 - 5 = 6 step 2: divide both sides by 2, we get x = 6/2 = 3 therefore, the solution is x = 3
Question 2: Solve the equation x/4 = 9 step 1: multiply both sides by 4, we get x = 9 × 4 = 36 therefore, the solution is x = 36
Question 3: Solve the equation x - 3 = 7 step 1: add 3 to both sides, we get x = 7 + 3 = 10 therefore, the solution is x = 10

🧠 The One Thing Most Students Get Wrong

most students get wrong the concept of solving linear equations with variables on both sides
for example, the equation 2x + 3 = 5x - 2 can be solved by first adding 2 to both sides, we get 2x + 5 = 5x
then, subtract 2x from both sides, we get 5 = 3x
finally, divide both sides by 3, we get x = 5/3
therefore, the solution is x = 5/3

👁️ Ayush's Note

to solve linear equations, first simplify the equation by combining like terms
then, isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation
finally, check the solution by plugging it back into the original equation
for example, to solve the equation 2x + 2 = 6, first subtract 2 from both sides, we get 2x = 4
then, divide both sides by 2, we get x = 2
therefore, the solution is x = 2

🔁 Last 5 Minutes Box

∈ the last 5 minutes of the exam, quickly review the formulas and concepts of linear equations
make sure to check the solutions by plugging them back into the original equations
also, make sure to write the final answers ∈ the correct format
for example, x = 2 instead of x = 2.0
quickly review the steps to solve linear equations, such as adding, subtracting, multiplying, or dividing both sides of the equation

📝 Practice MCQs

1. Question: Solve the equation x + 2 = 9

A) x = 7

B) x = 11

C) x = 10

D) x = 8

Answer: A) x = 7, because subtracting 2 from both sides gives x = 9 - 2 = 7

2. Question: Solve the equation 2x = 12

A) x = 5

B) x = 6

C) x = 4

D) x = 8

Answer: B) x = 6, because dividing both sides by 2 gives x = 12/2 = 6

3. Question: Solve the equation x - 1 = 3

A) x = 2

B) x = 4

C) x = 5

D) x = 6

Answer: B) x = 4, because adding 1 to both sides gives x = 3 + 1 = 4

4. Question: Solve the equation x/3 = 2

A) x = 5

B) x = 6

C) x = 4

D) x = 8

Answer: B) x = 6, because multiplying both sides by 3 gives x = 2 × 3 = 6

5. Question: Solve the equation 2x + 1 = 7

A) x = 2

B) x = 3

C) x = 4

D) x = 5

Answer: B) x = 3, because subtracting 1 from both sides gives 2x = 6, then dividing both sides by 2 gives x = 6/2 = 3

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides: