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Finding the Unknown - Mind the Mistake, Mend the Mistake

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An equation is a mathematical statement where the Left Hand Side (LHS) is equal to the Right Hand Side (RHS), separated by an '=' sign.

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The Transposition Rule: To find the unknown variable (like xx or yy), we move terms from one side to the other. When a term is transposed, its operation changes: addition becomes subtraction, and subtraction becomes addition.

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Mind the Mistake (Sign Change): A common error is moving a positive term to the other side without changing its sign. Always ensure x+a=bx + a = b becomes x=b−ax = b - a.

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Mind the Mistake (Multiplication/Division): When transposing a multiplier, it must divide the entire other side. For example, in 2x+4=102x + 4 = 10, you must subtract 44 first before dividing by 22.

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The Distributive Property: When a number is outside a bracket, such as 3(x−2)3(x - 2), it must be multiplied by every term inside the bracket to become 3x−63x - 6.

📐Formulae

x+a=b  ⟹  x=b−ax + a = b \implies x = b - a

x−a=b  ⟹  x=b+ax - a = b \implies x = b + a

ax=b  ⟹  x=baax = b \implies x = \frac{b}{a}

xa=b  ⟹  x=b×a\frac{x}{a} = b \implies x = b \times a

a(x+b)=ax+aba(x + b) = ax + ab

💡Examples

Problem 1:

Solve for xx: 4x+7=194x + 7 = 19

Solution:

4x=19−74x = 19 - 7 4x=124x = 12 x=124x = \frac{12}{4} x=3x = 3

Explanation:

Mind the Mistake: Students often add 77 to 1919 instead of subtracting. Mend the Mistake: Since 77 is added on the LHS, it must be subtracted when moved to the RHS. Finally, divide by 44 to isolate xx.

Problem 2:

Solve for yy: 3(y−5)=213(y - 5) = 21

Solution:

3y−15=213y - 15 = 21 3y=21+153y = 21 + 15 3y=363y = 36 y=363y = \frac{36}{3} y=12y = 12

Explanation:

Mind the Mistake: A common error is writing 3y−5=213y - 5 = 21, forgetting to multiply 33 by 55. Mend the Mistake: Use the distributive property: 3×y3 \times y and 3×(−5)3 \times (-5) to get 3y−153y - 15.

Problem 3:

Solve for zz: z2−10=5\frac{z}{2} - 10 = 5

Solution:

z2=5+10\frac{z}{2} = 5 + 10 z2=15\frac{z}{2} = 15 z=15×2z = 15 \times 2 z=30z = 30

Explanation:

Mind the Mistake: Do not multiply by 22 before transposing the −10-10. Mend the Mistake: First, move the constant −10-10 to the RHS by adding it to 55. Then, multiply by 22 to solve for zz.

Problem 4:

Check the calculation for transposing 1515 from x+15=40x + 15 = 40:

Solution:

40−1525\begin{array}{r} 40 \\ -15 \\ \hline 25 \end{array} x=25x = 25

Explanation:

To solve x+15=40x + 15 = 40, we subtract 1515 from 4040 using vertical subtraction to ensure accuracy.