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NCERT Solutions for Class 7th Maths Chapter 7 .3 Mind the Mistake, Mend the Mistake — Mind the Mistake, Mend the Mistake

Book page 181 – 1827 Updated on2026-09-19

Q1.
Go through each solution and decide whether the steps are correct. If there is a mistake, describe the mistake, correct it and solve the equation. 4x + 6 = 10 / 4x = 10 + 6 / 4x = 16 / x = 4
Answer

There is a mistake in the first step. The correct answer is x = 1.

The mistake: the term + 6 was removed from the LHS but was written as + 6 on the RHS. When a term is removed from one side, its additive inverse must appear on the other side — so it should be − 6.

Correct solution
4x + 6 = 10
4x = 10 − 6 = 4
x = 4 ÷ 4 = 1
Check: 4 × 1 + 6 = 4 + 6 = 10 ✓  (the wrong answer 4 gives 4 × 4 + 6 = 22, not 10)
Why it happens: think of the balance. To take a 6 kg weight off the left pan you must also take 6 kg off the right pan, not add it. That is why 10 becomes 10 − 6.
Q2.
7 – 8z = 5 / 8z = 7 – 5 / 8z = 2 / z = 4
Answer

The first two steps are fine; the last step is wrong. The correct answer is z = 1/4.

The mistake: from 8z = 2 the division was done the wrong way round — 8 was divided by 2 instead of 2 being divided by 8.

Correct solution
7 − 8z = 5
7 − 5 = 8z  (this step in the book is correct)
8z = 2
z = 2 ÷ 8 = 1/4
Check: 7 − 8 × (1/4) = 7 − 2 = 5 ✓  (z = 4 would give 7 − 32 = − 25)
Why it happens: to remove the factor 8 from the LHS you divide both sides by 8. The RHS is 2, so it becomes 2 ÷ 8. Dividing 8 by 2 is not the same operation at all.
Tip: a quick sanity check helps. Since 8z = 2 and 2 is smaller than 8, z must be smaller than 1.
Q3.
2v – 4 = 6 / v – 4 = 6 – 2 / v – 4 = 4 / v = 8
Answer

The first step is wrong. The correct answer is v = 5.

The mistake: 2v is a product, so the 2 is a factor, not a term. It cannot be moved across as a subtraction. To remove a factor you divide the whole of the other side by it.

Correct solution
2v − 4 = 6
2v = 6 + 4 = 10  (remove the term − 4 first)
v = 10 ÷ 2 = 5
Check: 2 × 5 − 4 = 10 − 4 = 6 ✓  (v = 8 gives 16 − 4 = 12)
Why it happens: terms and factors are removed by different operations — terms by adding the inverse, factors by dividing. Mixing them up is the single most common slip in this chapter. Ask yourself: is this number added to the unknown, or multiplied by it?
Q4.
5z + 2 = 3z – 4 / 5z + 3z = – 4 + 2 / 8z = – 2 / z = – 2/8
Answer

Both signs in the first step are wrong. The correct answer is z = − 3.

The mistake: 3z was moved to the LHS but its sign was not changed (it should become − 3z), and + 2 was moved to the RHS but also kept its sign (it should become − 2).

Correct solution
5z + 2 = 3z − 4
5z − 3z + 2 = − 4  (subtract 3z from both sides)
2z + 2 = − 4
2z = − 4 − 2 = − 6  (subtract 2 from both sides)
z = − 6 ÷ 2 = − 3
Check: LHS = 5(− 3) + 2 = − 13. RHS = 3(− 3) − 4 = − 13 ✓
Why it happens: "taking a term across" is shorthand for subtracting it from both sides. If you write the full step out — 5z + 2 − 3z = 3z − 4 − 3z — the sign takes care of itself. Shortcuts are only safe once you can write the long form.
Q5.
15w – 4w = 26 / 15w = 26 + 4w / 15w = 30 / w = 2
Answer

The working goes wrong from the second step onwards. The correct answer is w = 26/11.

The mistake: the LHS was already simplified — 15w − 4w is simply 11w. Instead the 4w was moved to the RHS, and then, worse, "26 + 4w" was replaced by the number 30, as though w were 1.

Correct solution
15w − 4w = 26
11w = 26  (collect the like terms on the LHS)
w = 26/11
Check: 15 × 26/11 − 4 × 26/11 = 390/11 − 104/11 = 286/11 = 26 ✓  (w = 2 gives 30 − 8 = 22)
Why it happens: 15w and 4w are like terms — they count the same thing, so they can be combined at once. Moving a term across the '=' is only needed when the unknown is on both sides, which it was not here. And 26 + 4w can never be turned into 30 unless w is known to be 1.
Q6.
3x + 1 = – 12 / x + 1 = – 12/3 / x + 1 = – 4 / x = – 5
Answer

The first step is wrong. The correct answer is x = − 13/3.

The mistake: both sides were divided by 3, but on the LHS only the 3x was divided. The 1 was left untouched. Dividing a side means dividing every term of it.

Correct solution
3x + 1 = − 12
3x = − 12 − 1 = − 13  (remove the term 1 first)
x = − 13 ÷ 3 = − 13/3
If you do prefer to divide first:
x + 1/3 = − 4, so x = − 4 − 1/3 = − 13/3 — the same answer.
Check: 3 × (− 13/3) + 1 = − 13 + 1 = − 12 ✓  (x = − 5 gives − 15 + 1 = − 14)
Why it happens: the LHS 3x + 1 is a sum, not a single product. Dividing a sum by 3 divides both parts: (3x + 1) ÷ 3 = x + 1/3. Removing the term before the factor avoids the trap altogether.
Q7.
4 (4q + 2) = 50 / 4 (4q) = 50 – 2 / 16q = 48 / q = 3
Answer

The first step is wrong. The correct answer is q = 21/8.

The mistake: the 2 inside the bracket is multiplied by 4, so it is worth 8, not 2. You cannot pull it out of the bracket unchanged.

Correct solution
4(4q + 2) = 50
16q + 8 = 50  (open the bracket: 4 × 4q and 4 × 2)
16q = 50 − 8 = 42
q = 42 ÷ 16 = 21/8
Or divide by 4 first: 4q + 2 = 50/4 = 25/2, so 4q = 25/2 − 2 = 21/2 and q = 21/8 — the same.
Check: 4(4 × 21/8 + 2) = 4(21/2 + 2) = 4 × 25/2 = 50 ✓  (q = 3 gives 4 × 14 = 56)
Why it happens: a number in front of a bracket multiplies everything inside it. Either open the bracket completely, or divide the whole equation by that number — but never take just one piece out.
Q8.
– 2 (3 – 4x) = 14 / –6v – 8x = 14 / – 8x = 14 + 6 / – 8x = 20 / x = – 20/8
Answer

There are several mistakes. The correct answer is x = 5/2.

  • A stray letter v has appeared: − 2 × 3 is the number − 6, not − 6v.
  • The sign is wrong: − 2 × (− 4x) = + 8x, not − 8x.
  • The term − 6 was then removed as though it were + 6.
Correct solution
− 2(3 − 4x) = 14
− 6 + 8x = 14  (− 2 × 3 = − 6 and − 2 × (− 4x) = + 8x)
8x = 14 + 6 = 20
x = 20 ÷ 8 = 5/2
Check: − 2(3 − 4 × 5/2) = − 2(3 − 10) = − 2 × (− 7) = 14 ✓
Why it happens: multiplying by a negative number changes the sign of every term inside the bracket. Writing the two products separately — (− 2) × 3 and (− 2) × (− 4x) — makes the signs hard to get wrong.
Q9.
3 (7y + 4) = 9 + 5y / 7y + 4 = 9/3 + 5y / 7y + 4 = 3 + 5y / 7y – 5y + 4 = 3 / 2y = 4 – 3 / y = 1/2
Answer

Two mistakes. The correct answer is y = − 3/16.

  • Both sides were divided by 3, but on the RHS only the 9 was divided — the 5y was left alone. It should have become 5y/3.
  • Later, "2y + 4 = 3" was turned into 2y = 4 − 3 instead of 2y = 3 − 4.
Correct solution
3(7y + 4) = 9 + 5y
21y + 12 = 9 + 5y  (open the bracket)
21y − 5y + 12 = 9  (subtract 5y from both sides)
16y + 12 = 9
16y = 9 − 12 = − 3
y = − 3 ÷ 16 = − 3/16
Check: LHS = 3(7 × (− 3/16) + 4) = 3(− 21/16 + 64/16) = 3 × 43/16 = 129/16
RHS = 9 + 5 × (− 3/16) = 144/16 − 15/16 = 129/16 ✓
Why it happens: the safest first move with a bracket is to open it, not to divide — dividing only helps when every term on the other side is divisible too. And when a term is removed from a side, its inverse appears on the other side: from 2y + 4 = 3 you get 2y = 3 − 4, which is − 1, not + 1.
Note: the answer is y = − 3/16. Opening the bracket first, as above, keeps every step in whole numbers until the final division.
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