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Solving Equations Quiz - CBSE Class 9 Mathematics

Free practice quiz: Solving Equations (CBSE Class 9 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 11 multiple-choice questions on Solving Equations, and 11 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: 11 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

Keep the equation balanced

An equation is like a balance: both sides have equal value.
Whatever you add, subtract, multiply or divide on one side, do the same on the other side.

Add same quantity

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

Subtract same quantity

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

Multiply by same quantity

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

Divide by same nonzero quantity

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

Common mistake: Changing only one side of the equation, for example subtracting a number from the left side but forgetting to subtract it from the right.

Transposing terms across the equals sign

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

Remove an added term

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

Remove a subtracted term

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

Remove a multiplier (a nonzero)

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

Common mistake: Moving a term across the equals sign without changing its sign, such as writing x + a = b as x = b + a.

Solving equations like ax + b = c

First move the constant term b to the other side, leaving the x-term alone.
Then divide both sides by the coefficient a to get x.

Isolate the x-term

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

General solution (a nonzero)

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

With a subtracted constant

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

Common mistake: Dividing only the x-term by a and not the whole other side, or dividing before moving the constant.

Equations with brackets

Open brackets using the distributive law: multiply the outside number with every term inside.
Or divide both sides by the outside number first, then solve the simpler equation.

Distributive law

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

Distributive law with minus

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

Divide first (a nonzero)

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

Bracket on the right side

\[c = a(x - b) \Leftrightarrow a(x - b) = c\]

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

Exam tips

Always check your answer by substituting x back into the original equation; both sides must be equal.
If the variable is on the right side, simply swap the two sides first.
Write each step on a new line so sign errors are easy to spot.

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 2x + 3 = 7?
Show answer
Answer: B. 2
To find x, we subtract 3 from both sides: 2x = 7 - 3 = 4. Then divide by 2: x = 4 / 2 = 2.
If 3x + 7 = 16, what is the value of x?
Show answer
Answer: A. 3
Subtract 7 from both sides: 3x = 16 - 7 = 9. Then divide by 3: x = 9 / 3 = 3.
What is the solution to x + 5 = 12?
Show answer
Answer: C. 7
Subtract 5 from both sides: x = 12 - 5 = 7.
What is the solution to 5x + 2 = 17?
Show answer
Answer: A. 3
Subtract 2 from both sides: 5x = 17 - 2 = 15. Then divide by 5: x = 15 / 5 = 3.
Find x if 3(x - 1) = 6.
Show answer
Answer: A. 3
Divide both sides by 3: x - 1 = 6 / 3 = 2. Then add 1: x = 2 + 1 = 3.

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