(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.) Show (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.) Answer:(i) Let Parmit has m marbles. 5 × Number of marbles Parmit has + 7 = Number of marbles Irfan has 5 × m + 7 = 37 5m + 7 = 37 (ii) Let Laxmi be y years old. 3 × Laxmi’s age + 4 = Laxmi’s father’s age 3 × y + 4 = 49 3y + 4 = 49 (iii) Let the lowest marks be l. 2 × Lowest marks + 7 = Highest marks 2 × l + 7 = 87 2 l + 7 = 87 (iv) An isosceles triangle has two of its angles of equal measure. Let base angle be b. Vertex angle = 2 × Base angle = 2b Sum of all interior angles of a Δ = 180° b + b + 2b = 180° 4b = 180° Video Solution for simple equations (Page: 82 , Q.No.: 6)NCERT Solution for Class 7 math - simple equations 82 , Question 6 Page No 86:Question 1: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 Answer:(a) x − 1 = 0 Adding 1 to both sides of the given equation, we obtain x − 1 + 1 = 0 + 1 x = 1 (b) x + 1 = 0 Subtracting 1 from both sides of the given equation, we obtain x + 1 − 1 = 0 − 1 x = −1 (c) x − 1 = 5 Adding 1 to both sides of the given equation, we obtain x − 1 + 1 = 5 + 1 x = 6 (d) x + 6 = 2 Subtracting 6 from both sides of the given equation, we obtain x + 6 − 6 = 2 − 6 x = −4 (e) y − 4 = −7 Adding 4 to both sides of the given equation, we obtain y − 4 + 4 = − 7 + 4 y = −3 (f) y − 4 = 4 Adding 4 to both sides of the given equation, we obtain y − 4 + 4 = 4 + 4 y = 8 (g) y + 4 = 4 Subtracting 4 from both sides of the given equation, we obtain y + 4 − 4 = 4 − 4 y = 0 (h) y + 4 = −4 Subtracting 4 from both sides of the given equation, we obtain y + 4 − 4 = − 4 − 4 y = −8 Page No 86:Question 2:Give first the step you will use to separate the variable and then solve the equation: (a) 3l = 42 (b)  (d) 4x = 25 (e) 8y = 36 (f) (g) Answer:(a) 3l = 42 Dividing both sides of the given equation by 3, we obtain l = 14 (b) Multiplying both sides of the given equation by 2, we obtain b = 12 (c) Multiplying both sides of the given equation by 7, we obtain p = 28 (d) 4x = 25 Dividing both sides of the given equation by 4, we obtain x = (e) 8y = 36 Dividing both sides of the given equation by 8, we obtain y = (f) Multiplying both sides of the given equation by 3, we obtain (g) Multiplying both sides of the given equation by 5, we obtain (h) 20t = −10 Dividing both sides of the given equation by 20, we obtain Page No 86:Question 3:Give the steps you will use to separate the variable and then solve the equation: (a) 3n − 2 = 46 (b) 5m + 7 = 17 (c) (d) Answer:(a) 3n − 2 = 46 Adding 2 to both sides of the given equation, we obtain 3n − 2 + 2 = 46 + 2 3n = 48 Dividing both sides of the given equation by 3, we obtain n = 16 (b) 5m + 7 = 17 Subtracting 7 from both sides of the given equation, we obtain 5m + 7 − 7 = 17 − 7 5m = 10 Dividing both sides of the given equation by 5, we obtain (c) Multiplying both sides of the given equation by 3, we obtain Dividing both sides of the given equation by 20, we obtain (d) Multiplying both sides of the given equation by 10, we obtain Dividing both sides of the given equation by 3, we obtain p = 20 Page No 86:Question 4:Solve the following equations: (a) 10p = 100 (b) 10p + 10 = 100 (c) (d) (g) 3s + 12 = 0 (h) 3s = 0 (i) 2q = 6 (j) 2q − 6 = 0 (k) 2q + 6 = 0 (l) 2q + 6 = 12 Answer:(a) 10 p = 100 (b) 10 p + 10 = 100 10 p + 10 − 10 = 100 − 10 10 p = 90 (c) (d) (e) (f) 3 s = −9 (g) 3 s + 12 = 0 3 s + 12 − 12= 0 − 12 3 s = −12 (h) 3 s = 0 (i) 2q = 6 (j) 2q − 6 = 0 2q − 6 + 6 = 0 + 6 2q = 6 (k) 2q + 6 = 0 2q + 6 − 6 = 0 − 6 2q = −6 (l) 2q + 6 = 12 2q + 6 − 6 = 12 − 6 2q = 6 Page No 89:Question 1:Solve the following equations. (a) (d) (g) (j) Answer:(a) Dividing both sides by 2, (b) 5t + 28 = 10 5t = 10 − 28 = −18 (Transposing 28 to R.H.S.) Dividing both sides by 5, (c) Multiplying both sides by 5, a = −1 × 5 = −5 (d) Multiplying both sides by 4, q = −8 (e) Multiplying both sides by 2, 5x = −10 × 2 = −20 Dividing both sides by 5, (f) Multiplying both sides by 2, Dividing both sides by 5, (g) Dividing both sides by 7, (h) 6z + 10 = −2 6z = − 2 − 10 = −12 (Transposing 10 to R.H.S.) Dividing both sides by 6, (i) Multiplying both sides by 2, Dividing both sides by 3, (j) Multiplying both sides by 3, 2b = 8 × 3 = 24 Dividing both sides by 2, b == 12 Page No 89:Question 2:Solve the following equations. (a) 2 (x + 4) = 12 (b) 3 (n − 5) = 21 (c) 3 (n − 5) = − 21 (d) −4 (2 + x) = 8 (e) 4(2 − x) = 8 Answer:(a) 2 (x + 4) = 12 Dividing both sides by 2, x = 6 − 4 = 2 (Transposing 4 to R.H.S.) (b) 3 (n − 5) = 21 Dividing both sides by 3, n = 7 + 5 = 12 (Transposing −5 to R.H.S.) (c) 3 (n − 5) = −21 Dividing both sides by 3, n = − 7 + 5 = −2 (Transposing −5 to R.H.S.) (d) −4 (2 + x) = 8 Dividing both sides by −4, x = − 2 − 2 = −4 (Transposing 2 to R.H.S.) (e) 4 (2 − x) = 8 Dividing both sides by 4, 2 − x = 2 −x = 2 − 2 (Transposing 2 to R.H.S.) −x = 0 x = 0 Page No 89:Question 3:Solve the following equations. (a) 4 = 5 (p − 2) (b) − 4 = 5 (p − 2) (c) 16 = 4 + 3 (t + 2) (d) 4 + 5 (p − 1) = 34 (e) 0 = 16 + 4 (m − 6) Answer:(a) 4 = 5 (p − 2) Dividing both sides by 5, (b) − 4 = 5 (p − 2) Dividing both sides by 5, (c) 16 = 4 + 3 (t + 2) 16 − 4 = 3 (t + 2) (Transposing 4 to L.H.S.) 12 = 3 (t + 2) Dividing both sides by 3, 4 = t + 2 4 − 2 = t (Transposing 2 to L.H.S.) 2 = t (d) 4 + 5 (p − 1) = 34 5 (p − 1) = 34 − 4 = 30 (Transposing 4 to R.H.S.) Dividing both sides by 5, p = 6 + 1 = 7 (Transposing −1 to R.H.S.) (e) 0 = 16 + 4 (m − 6) 0 = 16 + 4m − 24 0 = −8 + 4m 4m = 8 (Transposing −8 to L.H.S) Dividing both sides by 4, m = 2 Page No 89:Question 4:(a) Construct 3 equations starting with x = 2 (b) Construct 3 equations starting with x = − 2 Answer:(a) x = 2 Multiplying both sides by 5, 5x = 10 (i) Subtracting 3 from both sides, 5x − 3 = 10 − 3 5 x − 3 = 7 (ii) Dividing both sides by 2, (b) x = −2 Subtracting 2 from both sides, x − 2 = − 2 − 2 x − 2 = −4 (i) Again, x = −2 Multiplying by 6, 6 × x = −2 × 6 6x = −12 Subtracting 12 from both sides, 6x − 12 = − 12 − 12 6x − 12 = −24 (ii) Adding 24 to both sides, 6x − 12 + 24 = − 24 + 24 6x + 12 = 0 (iii) Page No 91:Question 1: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 fromof the number, the result is 23. Answer:(a) Let the number be x. 8 times of this number = 8x 8x + 4 = 60 8x = 60 − 4 (Transposing 4 to R.H.S.) 8x = 56 Dividing both sides by 8, (b) Let the number be x. One-fifth of this number = Multiplying both sides by 5, (c) Let the number be x. Three-fourth of this number = Multiplying both sides by 4, Dividing both sides by 3, (d) Let the number be x. Twice of this number = 2x 2x − 11 = 15 2x = 15 + 11 (Transposing −11 to R.H.S.) 2x = 26 Dividing both sides by 2, x = 13 (e) Let the number of books be x. Thrice the number of books = 3x 50 − 3x = 8 − 3x = 8 −50 (Transposing 50 to R.H.S.) −3x = −42 Dividing both sides by −3, (f) Let the number be x. Multiplying both sides by 5, x + 19 = 40 x = 40 − 19 (Transposing 19 to R.H.S.) x = 21 (g) Let the number be x. of this number = Multiplying both sides by 2, Dividing both sides by 5, Page No 91:Question 2: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°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°). (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? Answer:(a) Let the lowest score be l. 2 × Lowest marks + 7 = Highest marks 2l + 7 = 87 2l = 87 − 7 (Transposing 7 to R.H.S.) 2l = 80 Dividing both sides by 2, Therefore, the lowest score is 40. (b) Let the base angles be equal to b. The sum of all interior angles of a triangle is 180°. b + b + 40° = 180° 2b + 40° = 180° 2b = 180º − 40º = 140º (Transposing 40º to R.H.S.) Dividing both sides by 2, Therefore, the base angles of the triangle are of 70º measure. (c) Let Rahul’s score be x. Therefore, Sachin’s score = 2x Rahul’s score + Sachin’s score = 200 − 2 2x + x = 198 3x = 198 Dividing both sides by 3, x = 66 Rahul’s score = 66 Sachin’s score = 2 × 66 = 132 Video Solution for simple equations (Page: 91 , Q.No.: 2)NCERT Solution for Class 7 math - simple equations 91 , Question 2 Page No 91:Question 3: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 year 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 was 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? What is the solution to 2 2.2 x 3.3 6.6 x 3 x 3 x 3 or x 0 x 0 or x 3?x = -3, x = 3, x = -3, x = 0. Now, when we will remove the absolute value term it will create a (+/-) sign on the right side of the equation. ⇒ Hence the required solution is x = 3 and x = 0.
What is the value of x in the equation 2 x 3 9 3 1 )+ x?The value of x in the equation 2(x - 3) + 9 = 3(x + 1) + x is 0. 3 = 3.
What's the value of X?The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try!
What is the value of x in the equation 1.5 x 4 3 4.5 x 2?Summary: The value of x satisfying the equation 1.5(x + 4) - 3 = 4.5(x - 2) is 4.
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