Quizzes / CBSE / Class 8 / Mathematics / Linear Equations in One Variable

Solving Equations with Linear Expressions on One Side Quiz - CBSE Class 8 Mathematics

Free practice quiz: Solving Equations with Linear Expressions on One Side (CBSE Class 8 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 13 multiple-choice questions on Solving Equations with Linear Expressions on One Side, and 13 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Start quiz: 13 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

Balance and transpose terms

An equation is like a balance: do the same operation to both sides to keep it equal.
Transposing means moving a term to the other side and changing its sign: plus becomes minus, minus becomes plus.
First move the constant term, then divide by the coefficient of the variable.

Move an added constant

\[x + b = c \Rightarrow x = c - b\]

Move a subtracted constant

\[x - b = c \Rightarrow x = c + b\]

Divide by the coefficient

\[ax = d \Rightarrow x = \frac{d}{a},\; a \neq 0\]

General solution

\[ax + b = c \Rightarrow x = \frac{c - b}{a},\; a \neq 0\]

Common mistake: Moving a term across the equals sign without changing its sign, for example writing x = c + b from x + b = c.

Removing brackets correctly

Multiply the number outside the bracket by every term inside it. This is the distributive property.
Or divide both sides by the number outside first, then solve the simpler equation.

Distributive property

\[a(x + b) = ax + ab\]

Distributive property with minus

\[a(x - b) = ax - ab\]

Divide first

\[a(x + b) = c \Rightarrow x + b = \frac{c}{a},\; a \neq 0\]

Common mistake: Multiplying only the first term inside the bracket, for example writing a(x + b) as ax + b instead of ax + ab.

Clearing fractions and decimals

Multiply every term on both sides by the denominator, or by the LCM of all denominators.
For decimals, multiply every term by 100 or 1000 to make all numbers whole.
When the variable has a fractional coefficient, multiply both sides by its reciprocal.

Fractional coefficient

\[\frac{p}{q}x = r \Rightarrow x = \frac{q}{p} \times r\]

Expression over a denominator

\[\frac{x + b}{q} = r \Rightarrow x + b = qr\]

Common mistake: Multiplying only the fraction term by the LCM and forgetting to multiply the other terms on both sides.

Equations with absolute value

|E| is the distance of E from zero, so it is never negative.
If |E| = k with k positive, then E equals k or E equals negative k. Solve both cases.

Split into both cases

\[|E| = k,\; k > 0 \Rightarrow E = k \text{ or } E = -k\]

Zero case

\[|E| = 0 \Rightarrow E = 0\]

No solution

\[|E| = k,\; k < 0 \Rightarrow \text{no solution}\]

Common mistake: Solving only E = k and forgetting the second case E = -k. This misses an answer.

Exam tips

Check every answer by substituting it back into the original equation.
Write each step on a new line so you can catch sign errors.
For absolute value questions, check both answers in the original equation.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

Solve for x: 2x + 5 = 11
Show answer
Answer: A. x = 3
Subtract 5 from both sides: 2x = 6. Then divide both sides by 2: x = 3
Solve for a: 5a + 12 = 27
Show answer
Answer: A. a = 3
Subtract 12 from both sides: 5a = 15. Then divide both sides by 5: a = 3
Solve for y: 3(y - 2) = 18
Show answer
Answer: A. y = 8
Distribute the 3: 3y - 6 = 18. Add 6 to both sides: 3y = 24. Divide by 3: y = 8
Solve for n: 2/3n - 5 = 1
Show answer
Answer: A. n = 9
Add 5 to both sides: 2/3n = 6. Multiply both sides by 3/2: n = 9
Solve for x: (x+2)/3 + 1 = 5
Show answer
Answer: B. x = 10
Subtract 1 from both sides: (x+2)/3 = 4. Multiply both sides by 3: x+2 = 12. Subtract 2 from both sides: x = 10

Take the full quiz

More quizzes

Applications and Word Problems ▶ Play

Browse all Linear Equations in One Variable quizzes

More to play

Daily ChallengeA new quiz every day. Keep your streak.HangmanGuess the word, letter by letter.Story QuestLearn through short interactive stories.All quizzesCBSE, ICSE, competitive exams and more.