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Simple Equations Quiz - CBSE Class 6 Mathematics

Free practice quiz: Simple Equations (CBSE Class 6 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 13 multiple-choice questions on Simple Equations, 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.

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Equation and Its Solution

An equation says two sides are equal, like a balanced weighing scale with a variable on it.
The solution is the value of the variable that makes the left side equal to the right side.

General form

\[\text{LHS} = \text{RHS}\]

Sides can be swapped

\[\text{If } c = ax + b \text{, then } ax + b = c\]

Common mistake: Thinking an equation with the variable on the right side is different. You can simply swap the two sides.

Same Operation on Both Sides

To keep the balance, whatever you do to one side, you must do to the other side.
You may add, subtract, multiply or divide both sides by the same number, but never divide by zero.

Add to both sides

\[a = b \Rightarrow a + c = b + c\]

Subtract from both sides

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

Multiply both sides

\[a = b \Rightarrow a \times c = b \times c\]

Divide both sides (c not zero)

\[a = b \Rightarrow \frac{a}{c} = \frac{b}{c}\]

Common mistake: Doing an operation on only one side, for example subtracting a number from the left side but forgetting to subtract it from the right.

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 to the other side without changing its sign, like keeping plus as plus after transposing.

Solving Two-Step Equations

First remove the number added or subtracted, then remove the number multiplying the variable.
If the variable term has a minus sign, move it to the other side so it becomes positive.

Two-step rule

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

Minus variable term

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

Common mistake: Dividing before subtracting, so only part of the side gets divided, giving a wrong answer.

Equations with Brackets

Open the bracket by multiplying the outside number with every term inside, then solve as usual.
Or first divide both sides by the number outside the bracket, if it divides evenly.

Opening brackets

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

Divide first

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

Bracket with minus

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

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

Exam tips

Always check your answer by putting it back into the original equation.
Combine number terms on the same side before moving anything across the equals sign.
Write each step on a new line to avoid sign errors.

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

Sample questions

What is the value of x in the equation x + 5 = 10?
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Answer: A. 5
To find x, we subtract 5 from both sides of the equation: x = 10 - 5, which gives x = 5.
What is the solution for 2x - 3 = 7?
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Answer: C. 5
Add 3 to both sides: 2x = 10, then divide by 2 to get x = 5.
If 6a = 48, what is the value of a?
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Answer: B. 8
Divide both sides by 6: a = 48 / 6, which equals 8.
What is the solution for 9 - 3y = 0?
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Answer: D. 3
Subtract 9 from both sides: -3y = -9, then divide by -3 to get y = 3.
In the equation 12 = 3(2y + 2), what is y?
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Answer: B. 1
Expand the equation to get 12 = 6y + 6. Subtract 6 from both sides to obtain 6 = 6y. Divide both sides by 6 to find y = 1.