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Linear Equations Quiz - CBSE Class 7 Mathematics

Free practice quiz: Linear Equations (CBSE Class 7 Mathematics). 14 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 14 multiple-choice questions on Linear Equations, and 14 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: 14 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

What is a Linear Equation

A linear equation has one variable, like x, with power one, and an equals sign joining two sides.
The solution is the value of x that makes the left side (LHS) equal the right side (RHS).

General form (a is not zero)

\[ax + b = c\]

Solution of the general form

\[x = \frac{c - b}{a}\]

Common mistake: Thinking an equation has many answers. A linear equation in one variable has exactly one solution.

Balance Both Sides Equally

An equation is like a balanced weighing scale. Whatever you do to one side, do to the other.
You may add, subtract, multiply or divide both sides by the same number, but never divide by zero.

Add the same number

\[p = q \Rightarrow p + c = q + c\]

Subtract the same number

\[p = q \Rightarrow p - c = q - c\]

Multiply by the same number

\[p = q \Rightarrow pc = qc\]

Divide by the same non-zero number

\[p = q \Rightarrow \frac{p}{c} = \frac{q}{c}\]

Common mistake: Changing only one side of the equation, for example subtracting from the LHS but forgetting to subtract from the RHS.

Transposing Terms Changes Sign

Moving a term to the other side is called transposing. Its operation turns into the opposite operation.
Plus becomes minus, minus becomes plus, multiply becomes divide, and divide becomes multiply.

Plus becomes minus

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

Minus becomes plus

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

Multiply becomes divide

\[ax = b \Rightarrow x = \frac{b}{a}\]

Divide becomes multiply

\[\frac{x}{a} = b \Rightarrow x = ab\]

Common mistake: Moving a term across the equals sign without changing its sign, so the term keeps its plus or minus sign.

Brackets, Order and Checking

If the equation has brackets, first open them by multiplying the outside number with each term inside.
The variable may sit on the right side. You can swap the sides, because p = q means q = p.

Opening brackets

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

Swapping the sides

\[c = ax + b \iff ax + b = c\]

Variable term first

\[c - ax = b \Rightarrow ax = c - b\]

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

Exam tips

Check your answer by putting it back into the equation. Both sides must come out equal.
Answers can be negative numbers or fractions, so do not reject them.
First move the number terms to one side, then divide by the coefficient of x.

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

Sample questions

What is the solution to the equation 2x + 3 = 7?
Show answer
Answer: B. x = 2
To solve 2x + 3 = 7, subtract 3 from both sides to get 2x = 4. Then divide by 2 to find x = 2.
If 4x - 8 = 0, then x equals?
Show answer
Answer: C. x = 2
Add 8 to both sides to get 4x = 8. Dividing by 4 gives x = 2.
If 2x + 4 = 10, what is the value of x?
Show answer
Answer: A. x = 3
First, subtract 4 from both sides to get 2x = 6. Next, divide by 2 to find x = 3.
If 7x + 3 = 24, what is x?
Show answer
Answer: B. x = 3
Subtract 3 from both sides: 7x = 21. Dividing by 7 gives x = 3.
What is the value of x in the equation 9x - 27 = 0?
Show answer
Answer: B. x = 3
Add 27 to both sides: 9x = 27. Dividing by 9 gives x = 3.

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