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Solving Equations Quiz - CBSE Class 7 Mathematics

Free practice quiz: Solving Equations (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 Solving Equations, 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.

Start quiz: 12 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

Keep the equation balanced

An equation is like a balance: the left side equals the right side.
Whatever you do to one side, do exactly the same to the other side.

Add the same to both sides

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

Subtract the same from both sides

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

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

Undo multiplication and division

If the variable is multiplied by a number, divide both sides by that number.
If the variable is divided by a number, multiply both sides by that number.

Divide both sides by a (a nonzero)

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

Multiply both sides by a

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

Common mistake: Subtracting the coefficient instead of dividing, for example treating ax = b as x = b - a.

Solve two-step equations in order

First remove brackets by multiplying every term inside by the number outside.
Then undo adding or subtracting, and finally undo multiplying or dividing.

Remove brackets

\[a(bx + c) = abx + ac\]

Two-step solving (a nonzero)

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

Fraction with a constant

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

Common mistake: Multiplying only the first term inside the bracket, writing a(bx + c) as abx + c.

Variables on both sides

Move all variable terms to one side and all number terms to the other side.
When a term moves across the equals sign, its sign changes (transposing).

Collect like terms

\[ax + b = cx + d \Rightarrow (a - c)x = d - b\]

Final step (a and c different)

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

Common mistake: Forgetting to change the sign when transposing, such as moving +cx to the left as +cx.

Exam tips

Check your answer by putting it back into the original equation; both sides must be equal.
Write one step per line so you do not lose a sign or term.
The answer can be a fraction or a negative number, not always a whole number.

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

Sample questions

Solve for x: x + 5 = 10
Show answer
Answer: B. 5
Subtract 5 from both sides to isolate x: x = 10 - 5, so x = 5.
Solve for z: 2z = 12
Show answer
Answer: B. 6
Divide both sides by 2 to solve for z: z = 12 / 2, so z = 6.
If 5b = 20, what is the value of b?
Show answer
Answer: B. 4
Divide both sides by 5 to get b: b = 20 / 5, so b = 4.
Solve for m: m/3 = 4
Show answer
Answer: D. 12
Multiply both sides by 3 to isolate m: m = 4 * 3, so m = 12.
What is q if 4q - 1 = 2q + 9?
Show answer
Answer: B. 5
Subtract 2q from both sides and add 1: 2q = 10, q = 5.

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