NCERT Solutions for Class 7th Maths Chapter 7 .2 Solving Equations Systematically — In-text Questions

Book page 169 – 1707 Updated on2026-09-19

Q1.

Consider an equation 15 + 8 = 23. If we add, subtract, multiply or divide the same number on both sides, will it still preserve the equality of LHS and RHS? For example, you can check by adding 10 to both sides.

Answer

Yes — the equality survives all four operations, as long as you do the same thing to both sides.

Operation	New LHS	New RHS	Still equal?
Add 10	15 + 8 + 10 = 33	23 + 10 = 33	Yes
Subtract 7	15 + 8 − 7 = 16	23 − 7 = 16	Yes
Multiply by 4	(15 + 8) × 4 = 92	23 × 4 = 92	Yes
Divide by 23	(15 + 8) ÷ 23 = 1	23 ÷ 23 = 1	Yes

Why it happens: the LHS and the RHS are not two different things — they are two names for the same number, 23. If you do the same thing to a number, you get the same answer, whichever name you started from. So the two sides can never drift apart. This is precisely the weighing-scale rule: remove (or add) equal weights on both pans and the scale stays balanced.

Tip: the one operation to be careful with is dividing by 0 — that is not allowed for any number. Everything else is safe.

Q2.

Example 1: It is known that 14593 – 1459 + 145 – 14 + 88 = 13353. What is the value of 14593 – 1459 + 145 – 14?

Answer

13265. And we do not have to evaluate the long expression at all.

14593 − 1459 + 145 − 14 + 88 = 13353
Subtract 88 from both sides:
14593 − 1459 + 145 − 14 + 88 − 88 = 13353 − 88
14593 − 1459 + 145 − 14 = 13265

Why it happens: addition and subtraction are inverse operations. The term + 88 on the LHS is cancelled by − 88, and that leaves exactly the expression we were asked about. Because we subtracted 88 from the RHS as well, the equality is untouched.

Check it yourself: 14593 − 1459 = 13134; 13134 + 145 = 13279; 13279 − 14 = 13265. And 13265 + 88 = 13353. ✓

Q3.

Example 2: It is known that 23 × 41 × 11 × 8 × 7 = 5,80,888. What is the value of the expression 23 × 41 × 11 × 8? Is this the same as dividing both sides by 7, which removes the factor 7 and leaves only the expression to be evaluated on the LHS?

Answer

82,984 — and yes, dividing 5,80,888 by 7 is exactly the same as dividing both sides by 7.

23 × 41 × 11 × 8 × 7 = 5,80,888
Divide both sides by 7:
(23 × 41 × 11 × 8 × 7) ÷ 7 = 5,80,888 ÷ 7
23 × 41 × 11 × 8 = 82,984

Why it happens: multiplication and division are inverse operations, so the factor 7 on the LHS is removed by dividing by 7. Doing the division "only on the right" and doing it "on both sides" are the same act described in two ways — on the left the division simply cancels the 7 and leaves nothing to compute.

Check it yourself: 82984 × 7 = 580888. ✓ (Also 23 × 41 = 943, 943 × 11 = 10373, 10373 × 8 = 82984.)

Q4.

Example 3: It is known that 12345 – 5432 + 135 – 24 – (–67) = 7091. What is the value of the expression 12345 – 5432 + 135 – 24?

Answer

7024.

12345 − 5432 + 135 − 24 − (−67) = 7091
Add (−67) to both sides — this is easier to picture than subtracting:
12345 − 5432 + 135 − 24 − (−67) + (−67) = 7091 + (−67)
The terms − (−67) and + (−67) cancel, so
12345 − 5432 + 135 − 24 = 7091 − 67 = 7024

Why it happens: − (−67) means "add 67", so its additive inverse is "add (−67)", that is, subtract 67. Putting the two together gives zero and the unwanted term disappears from the LHS. The RHS then loses 67 as well, keeping the equality.

Note: the book's working line prints 132 in place of 135. That is a slip — the figure given in the question is 135, and 12345 − 5432 + 135 − 24 = 7024, which is the answer the book itself states.

Check it yourself: 12345 − 5432 = 6913; 6913 + 135 = 7048; 7048 − 24 = 7024. And 7024 − (−67) = 7024 + 67 = 7091. ✓

Q5.

Example 4: It is known that (35/113) × 24 × 14 × (8/9) = 94080/1017. What is the value of the expression (35/113) × 24 × 14?

Answer

11760/113.

To keep only the wanted expression on the LHS we must remove the factor 8/9.
Divide both sides by 8/9, that is, multiply both sides by 9/8:

(35/113) × 24 × 14 × (8/9) × (9/8) = (94080/1017) × (9/8)
(8/9) × (9/8) = 1, so the LHS is just the expression we want

RHS = (94080 × 9) ÷ (1017 × 8) = 846720 ÷ 8136 = 11760/113

Why it happens: dividing by a fraction is the same as multiplying by its reciprocal. The pair (8/9) and (9/8) multiply to 1, so the factor vanishes from the LHS — exactly like taking a weight off a pan. The same multiplication done on the RHS keeps the two sides equal.

Check it yourself: (35/113) × 24 × 14 = (35 × 24 × 14)/113 = 11760/113. And (11760/113) × (8/9) = 94080/1017. ✓

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