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Algebraic Techniques Quiz - CBSE Class 7 Mathematics

Free practice quiz: Algebraic Techniques (CBSE Class 7 Mathematics). 12 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 12 multiple-choice questions on Algebraic Techniques, and 12 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.

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Learn the key ideas first ↓

Learn the key ideas Beta

Keep the Equation Balanced

An equation is like a balance. Both sides must stay equal.
Whatever you add, subtract, multiply or divide on one side, do the same on the other side.

Add or subtract the same number

\[a = b \Rightarrow a + c = b + c,\; a - c = b - c\]

Multiply the same number

\[a = b \Rightarrow ac = bc\]

Divide by the same non-zero number

\[a = b \Rightarrow \frac{a}{c} = \frac{b}{c},\; c \neq 0\]

Common mistake: Changing only one side of the equation, for example dividing the left side but forgetting to divide the right side.

Transposing Terms Across Sides

Moving a term to the other side changes its operation to the opposite one.
Plus becomes minus, minus becomes plus, multiply becomes divide, and divide becomes multiply.

Undo addition

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

Undo subtraction

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

Undo multiplication

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

Undo division

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

Common mistake: Moving a term across the equals sign without changing its sign or operation, like keeping a plus term as plus.

Solving Two-Step Equations

First remove the number added or subtracted. Then remove the number multiplying or dividing x.
Work in reverse order of operations to get x alone.

Multiply-then-add form

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

Divide-then-add form

\[\frac{x}{a} + b = c \Rightarrow x = a(c - b)\]

Common mistake: Dividing or multiplying first, before removing the added number, which gives a wrong value of x.

Brackets and Negative x Terms

For a bracket, divide both sides by the outside number, or expand using multiplication over brackets.
If x has a minus sign in front, move it to make it positive.

Expand a bracket

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

Bracket equation

\[a(x + b) = c \Rightarrow x = \frac{c}{a} - b\]

Negative x term

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

Negative multiple of x

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

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

Exam tips

Always check your answer by putting the value of x back into the original equation.
Write one step per line so you do not lose a sign.
Watch the sign before x; a negative x needs careful handling.

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

Sample questions

Solve the equation: 3x + 2 = 11
Show answer
Answer: C. x = 3
To solve 3x + 2 = 11, subtract 2 from both sides to get 3x = 9, then divide by 3 to get x = 3.
What is x if 2x + 5 = 15?
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Answer: B. x = 5
Subtract 5 from both sides to get 2x = 10, then divide by 2 to get x = 5.
Solve for x: 3(x + 4) = 21
Show answer
Answer: C. x = 3
First, divide both sides by 3 to get x + 4 = 7. Then subtract 4 from both sides to find x = 3.
What is x if x/4 = 5?
Show answer
Answer: C. x = 20
Multiply both sides by 4 to find x = 20.
What is the value of x if 3 - x = 2?
Show answer
Answer: B. x = 1
Subtract 3 from both sides to get -x = -1. Multiply by -1 to find x = 1.

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