CBSE · NCERT · Class 7 Maths · Chapter 4

NCERT Solutions: Class 7 Maths Chapter 4 - Simple Equations

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Chapter-wise NCERT intext questions and exercise answers for Simple Equations, grounded in the official textbook.

Questions are taken verbatim from the NCERT textbook; answers were grounded against the chapter's content during generation. Items needing review are marked.
Sections in this chapter
Exercise 4.1 1Exercise 4.2 1Exercise 4.3 1
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1Exercise 4.11 questions
Q.1-61. Complete the last column of the table. Say whether the equation is satisfied (Yes/No): (i) $x+3=0$, value $x=3$ (ii) $x+3=0$, value $x=0$ (iii) $x+3=0$, value $x=-3$ (iv) $x-7=1$, value $x=7$ (v) $x-7=1$, value $x=8$ (vi) $5x=25$, value $x=0$ (vii) $5x=25$, value $x=5$ (viii) $5x=25$, value $x=-5$ (ix) $\frac{m}{3}=2$, value $m=-6$ (x) $\frac{m}{3}=2$, value $m=0$ (xi) $\frac{m}{3}=2$, value $m=6$. 2. Check whether the value given in the brackets is a solution to the given equation or not: (a) $n+5=19$ $(n=1)$ (b) $7n+5=19$ $(n=-2)$ (c) $7n+5=19$ $(n=2)$ (d) $4p-3=13$ $(p=1)$ (e) $4p-3=13$ $(p=-4)$ (f) $4p-3=13$ $(p=0)$. 3. Solve the following equations by trial and error method: (i) $5p+2=17$ (ii) $3m-14=4$. 4. Write equations for the following statements: (i) The sum of numbers $x$ and 4 is 9. (ii) 2 subtracted from $y$ is 8. (iii) Ten times $a$ is 70. (iv) The number $b$ divided by 5 gives 6. (v) Three-fourth of $t$ is 15. (vi) Seven times $m$ plus 7 gets you 77. (vii) One-fourth of a number $x$ minus 4 gives 4. (viii) If you take away 6 from 6 times $y$, you get 60. (ix) If you add 3 to one-third of $z$, you get 30. 5. Write the following equations in statement forms: (i) $p+4=15$ (ii) $m-7=3$ (iii) $2m=7$ (iv) $\frac{m}{5}=3$ (v) $\frac{3m}{5}=6$ (vi) $3p+4=25$ (vii) $4p-2=18$ (viii) $\frac{p}{2}+2=8$. 6. Set up an equation in the following cases: (i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take $m$ to be the number of Parmit's marbles.) (ii) Laxmi's father is 49 years old. He is 4 years older than three times Laxmi's age. (Take Laxmi's age to be $y$ years.) (iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be $l$.) (iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be $b$ in degrees. Remember that the sum of angles of a triangle is 180 degrees).v
Solution

To check a solution, substitute the value into the equation. To set up an equation, translate each verbal operation into algebra using the unknown letter.

Answer:

1. (i) No (ii) No (iii) Yes (iv) No (v) Yes (vi) No (vii) Yes (viii) No (ix) No (x) No (xi) Yes.
2. (a) No (b) No (c) Yes (d) No (e) No (f) No.
3. (i) $p=3$ (ii) $m=6$.
4. (i) $x+4=9$ (ii) $y-2=8$ (iii) $10a=70$ (iv) $\frac{b}{5}=6$ (v) $\frac{3t}{4}=15$ (vi) $7m+7=77$ (vii) $\frac{x}{4}-4=4$ (viii) $6y-6=60$ (ix) $\frac{z}{3}+3=30$.
5. (i) The sum of $p$ and 4 is 15. (ii) 7 subtracted from $m$ is 3. (iii) Twice a number $m$ is 7. (iv) One-fifth of a number $m$ is 3. (v) Three-fifth of a number $m$ is 6. (vi) Three times a number $p$ when added to 4 gives 25. (vii) 2 subtracted from four times a number $p$ is 18. (viii) Add 2 to half of a number $p$ to get 8.
6. (i) $5m+7=37$ (ii) $3y+4=49$ (iii) $2l+7=87$ (iv) $4b=180^\circ$.

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2Exercise 4.21 questions
Q.1-41. Give first the step you will use to separate the variable and then solve the equation. 2. Give the steps you will use to separate the variable and then solve the equation. 3. Solve the equations given in paired form. 4. Solve the listed simple equations involving $p,s,q$.v
Solution

Use inverse operations on both sides. Addition undoes subtraction, subtraction undoes addition, multiplication undoes division and division undoes multiplication.

Answer:

1. (a) Add 1 to both sides; $x=1$ (b) Subtract 1 from both sides; $x=-1$ (c) Add 1 to both sides; $x=6$ (d) Subtract 6 from both sides; $x=-4$ (e) Add 4 to both sides; $y=-3$ (f) Add 4 to both sides; $y=8$ (g) Subtract 4 from both sides; $y=0$ (h) Subtract 4 from both sides; $y=-8$.
2. (a) Divide both sides by 3; $l=14$ (b) Multiply both sides by 2; $b=12$ (c) Multiply both sides by 7; $p=28$ (d) Divide both sides by 4; $x=\frac{25}{4}$ (e) Divide both sides by 8; $y=\frac{36}{8}$ (f) Multiply both sides by 3; $z=\frac{15}{4}$ (g) Multiply both sides by 5; $a=\frac{7}{3}$ (h) Divide both sides by 20; $t=\frac{1}{2}$.
3. (a) Add 2 to both sides, then divide by 3; $n=16$. (b) Subtract 7 from both sides, then divide by 5; $m=2$. (c) Multiply both sides by 3, then divide by 20; $p=6$. (d) Multiply both sides by 10, then divide by 3; $p=20$.
4. (a) $p=10$ (b) $p=9$ (c) $p=20$ (d) $p=-15$ (e) $p=8$ (f) $s=-3$ (g) $s=-4$ (h) $s=0$ (i) $q=3$ (j) $q=3$ (k) $q=-3$ (l) $q=3$.

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3Exercise 4.31 questions
Q.1-41. Set up equations and solve them to find the unknown numbers in statements (a) to (g). 2. Solve the word problems on lowest score, equal angles, and runs scored by Sachin and Rahul. 3. Solve the given age and number problems. 4. Solve the perimeter problem in the exercise.v
Solution

Translate each word problem into an equation, isolate the variable using inverse operations, and substitute back to check the value.

Answer:

1. (a) $8x+4=60$, $x=7$ (b) $\frac{x}{5}-4=3$, $x=35$ (c) $\frac{3y}{4}+3=21$, $y=24$ (d) $2m-11=15$, $m=13$ (e) $50-3x=8$, $x=14$ (f) $\frac{x+19}{5}=8$, $x=21$ (g) $\frac{5n}{2}-7=23$, $n=12$.
2. (a) Lowest score $=40$ (b) $70^\circ$ each (c) Sachin: 132 runs, Rahul: 66 runs.
3. (i) 6 (ii) 15 years (iii) 25.
4. 30.

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