# Simple Equations - Class 7 - Mathematics

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## Examples - Simple Equations | NCERT | Mathematics | Class 7

Write the following statements in the form of equations:

(i) The sum of three times $x$ and 11 is 32 .

(ii) If you subtract 5 from 6 times a number, you get 7 .

(iii) One fourth of $m$ is 3 more than 7 .

(iv) One third of a number plus 5 is 8 .

Let's write each statement as an equation.

(i) The statement "The sum of three times $x$ and 11 is 32" translates to: $$ 3x + 11 = 32 $$

(ii) The statement "If you subtract 5 from 6 times a number, you get 7" translates to: $$ 6x - 5 = 7 $$ where $x$ is the number referred to.

(iii) The statement "One fourth of $m$ is 3 more than 7" translates to: $$ \frac{1}{4}m = 7 + 3 $$

(iv) The statement "One third of a number plus 5 is 8" translates to: $$ \frac{1}{3}x + 5 = 8 $$ where $x$ is the number referred to.

Convert the following equations in statement form:

(i) $x-5=9$

(ii) $5 p=20$

(iii) $3 n+7=1$

(iv) $\frac{m}{5}-2=6$

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Sign up nowConsider the following situation:

Raju's father's age is 5 years more than three times Raju's age. Raju's father is 44 years old. Set up an equation to find Raju's age.

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Sign up nowA shopkeeper sells mangoes in two types of boxes, one small and one large. A large box contains as many as 8 small boxes plus 4 loose mangoes. Set up an equation which gives the number of mangoes in each small box. The number of mangoes in a large box is given to be 100 .

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Sign up nowSolve: (a) $3 n+7=25$ with steps

(b) $2 p-1=23$ with steps

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Solve: $12 p-5=25$

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Solve

(a) $4(m+3)=18$

(b) $-2(x+3)=8$

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The sum of three times a number and 11 is 32 . Find the number.

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Find a number, such that one-fourth of the number is 3 more than 7.

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Raju's father's age is 5 years more than three times Raju's age. Find Raju's age, if his father is 44 years old.

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## Exercise 4.1 - Simple Equations | NCERT | Mathematics | Class 7

Complete the last column of the table.

S. no. | Equation | Value | Say, whether the equation is satisfied. (Yes/ No) |
---|---|---|---|

(i) | $x+3=0$ | $x=3$ | |

(ii) | $x+3=0$ | $x=0$ | |

(iii) | $x+3=0$ | $x=-3$ | |

(iv) | $x-7=1$ | $x=7$ | |

(v) | $x-7=1$ | $x=8$ | |

(vi) | $5x=25$ | $x=0$ | |

(vii) | $5x=25$ | $x=5$ | |

(viii) | $5x=25$ | $x=-5$ | |

(ix) | $\frac{m}{3}=2$ | $m=-6$ | |

(x) | $\frac{m}{3}=2$ | $m=0$ | |

(xi) | $\frac{m}{3}=2$ | $m=6$ |

To complete the last column, let's evaluate whether the given value satisfies each equation:

- For $x+3=0$, $x=3$ does not satisfy the equation. Correct value: $x=-3$. Answer: No
- For $x+3=0$, $x=0$ does not satisfy the equation. Correct value: $x=-3$. Answer: No
- For $x+3=0$, $x=-3$ satisfies the equation. Answer: Yes
- For $x-7=1$, $x=7$ does not satisfy the equation. Correct value: $x=8$. Answer: No
- For $x-7=1$, $x=8$ satisfies the equation. Answer: Yes
- For $5x=25$, $x=0$ does not satisfy the equation. Correct value: $x=5$. Answer: No
- For $5x=25$, $x=5$ satisfies the equation. Answer: Yes
- For $5x=25$, $x=-5$ does not satisfy the equation. Correct value: $x=5$. Answer: No
- For $\frac{m}{3}=2$, $m=-6$ does not satisfy the equation. Correct value: $m=6$. Answer: No
- For $\frac{m}{3}=2$, $m=0$ does not satisfy the equation. Correct value: $m=6$. Answer: No
- For $\frac{m}{3}=2$, $m=6$ satisfies the equation. Answer: Yes

Check whether the value given in the brackets is a solution to the given equation or not:

(a) $n+5=19(n=1)$

(b) $7 n+5=19(n=-2)$

(c) $7 n+5=19(n=2)$

(d) $4 p-3=13(p=1)$

(e) $4 p-3=13(p=-4)$

(f) $4 p-3=13(p=0)$

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Solve the following equations by trial and error method:

(i) $5 p+2=17$

(ii) $3 m-14=4$

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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 .

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Write the following equations in statement forms:

(i) $p+4=15$

(ii) $m-7=3$

(iii) $2 m=7$

(iv) $\frac{m}{5}=3$

(v) $\frac{3 m}{5}=6$

(vi) $3 p+4=25$

(vii) $4 p-2=18$

(viii) $\frac{p}{2}+2=8$

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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).

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## Exercise 4.2 - Simple Equations | NCERT | Mathematics | Class 7

Give first the step you will use to separate the variable and then solve the equation:

(a) $x-1=0$

(b) $x+1=0$

(c) $x-1=5$

(d) $x+6=2$

(e) $y-4=-7$

(f) $y-4=4$

(g) $y+4=4$

(h) $y+4=-4$

To solve these equations for the variable (either $x$ or $y$), we will isolate the variable on one side of the equation. Here's the general strategy for each:

(a) **$x-1=0$**: Add $1$ to both sides to isolate $x$.

(b) **$x+1=0$**: Subtract $1$ from both sides to isolate $x$.

(c) **$x-1=5$**: Add $1$ to both sides to isolate $x$.

(d) **$x+6=2$**: Subtract $6$ from both sides to isolate $x$.

(e) **$y-4=-7$**: Add $4$ to both sides to isolate $y$.

(f) **$y-4=4$**: Add $4$ to both sides to isolate $y$.

(g) **$y+4=4$**: Subtract $4$ from both sides to isolate $y$.

(h) **$y+4=-4$**: Subtract $4$ from both sides to isolate $y$.

Now, let's solve these equations:

For (a) and (b), we solve by adding or subtracting $1$ directly.

For (c) and (d), we adjust by adding or subtracting to get $x$.

For (e), (f), (g), and (h), similar steps are followed, but we’re solving for $y$ instead.

Given the straightforward nature of these manipulations, I'll provide the solutions directly:

(a) $x = 1$

(b) $x = -1$

(c) $x = 6$

(d) $x = -4$

(e) $y = -3$

(f) $y = 8$

(g) $y = 0$

(h) $y = -8$

Give first the step you will use to separate the variable and then solve the equation:

(a) $3 l=42$

(b) $\frac{b}{2}=6$

(c) $\frac{p}{7}=4$

(d) $4 x=25$

(e) $8 y=36$

(f) $\frac{z}{3}=\frac{5}{4}$

(g) $\frac{a}{5}=\frac{7}{15}$

(h) $20 t=-10$

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Give the steps you will use to separate the variable and then solve the equation:

(a) $3 n-2=46$

(b) $5 m+7=17$

(c) $\frac{20 p}{3}=40$

(d) $\frac{3 p}{10}=6$

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Solve the following equations show the steps

(a) $10 p=100$

(b) $10 p+10=100$

(c) $\frac{p}{4}=5$

(d) $\frac{-p}{3}=5$

(e) $\frac{3 p}{4}=6$

(f) $3 s=-9$

(g) $3 s+12=0$

(h) $3 s=0$

(i) $2 q=6$

(j) $2 q-6=0$

(k) $2 q+6=0$

(l) $2 q+6=12$

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## Exercise 4.3 - Simple Equations | NCERT | Mathematics | Class 7

Set up equations and solve them to find the unknown numbers in the following cases:

(a) Add 4 to eight times a number; you get 60.

(b) One-fifth of a number minus 4 gives 3.

(c) If I take three-fourths of a number and add 3 to it, I get 21.

(d) When I subtracted 11 from twice a number, the result was 15.

(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8 .

(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8 .

(g) Anwar thinks of a number. If he takes away 7 from $\frac{5}{2}$ of the number, the result is 23 .

Here are the solutions for the given cases:

(a) **Add 4 to eight times a number; you get 60.**

- Equation: $8x + 4 = 60$
- Solution: $x = 7$

(b) **One-fifth of a number minus 4 gives 3.**

- Equation: $\frac{1}{5}x - 4 = 3$
- Solution: $x = 35$

(c) **If I take three-fourths of a number and add 3 to it, I get 21.**

- Equation: $\frac{3}{4}x + 3 = 21$
- Solution: $x = 24$

(d) **When I subtracted 11 from twice a number, the result was 15.**

- Equation: $2x - 11 = 15$
- Solution: $x = 13$

(e) **Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.**

- Equation: $50 - 3x = 8$
- Solution: $x = 14$

(f) **Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.**

- Equation: $\frac{x + 19}{5} = 8$
- Solution: $x = 21$

(g) **Anwar thinks of a number. If he takes away 7 from $\frac{5}{2}$ of the number, the result is 23.**

- Equation: $\frac{5}{2}x - 7 = 23$
- Solution: $x = 12$

Solve the following:

(a) 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. What is the lowest score?

(b) In an isosceles triangle, the base angles are equal. The vertex angle is $40^{\circ}$. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is $180^{\circ}$ ).

(c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

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Solve the following:

(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have?

(ii) Laxmi's father is 49 years old. He is 4 years older than three times Laxmi's age. What is Laxmi's age?

(iii) People of Sundargram planted trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted if the number of non-fruit trees planted was 77 ?

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Solve the following riddle:

I am a number,

Tell my identity!

Take me seven times over

And add a fifty!

To reach a triple century

$$ \text { You still need forty! } $$