Add 3 x - 2x + 4 and 2x + 3x - 5 [M-1]
Answers
Answer:
this is an example
Step-by-step explanation:
Exercise 2.1
Question 1:
Solve the following: x – 2= 7
Answer:
Given, x -2 = 7
=> x – 2 + 2= 7 + 2 [Adding 2 both sides]
=> x = 9
Question 2:
Solve of the following: y + 3 = 10
Solution:
Given, y + 3 = 10
=> y + 3 – 3 = 10 – 3 [subtracting 3 on both side]
=> y = 7
Question 3:
Solve the following: 6 = z + 2
Answer:
Given, 6 = 2 + z
=> 6 – 2 = z + 2 – 2 [Subtracting 2 both sides]
=> 4 = z
=> z = 4
Question 4:
Solve the following: 3/7 + x = 17/7
Answer:
Given, 3/7 + x = 17/7
=> 3/7 + x – 3/7 = 17/7 – 3/7 [Subtracting 3/7 on both sides]
=> x = (17 - 3)/7
=> x = 14/7
=> x = 2
Question 5:
Solve the following: 6x = 12
Answer:
Given, 6x = 12
=> 6x/6 = 12/6 [Dividing 6 on both side]
=> x = 2
Question 6:
Solve the following: t/5 = 10
Answer:
Given, t/5 = 10
=> t/5 * 5 = 10 * 5 [Multiply by 5 on both side]
=> t = 50
Question 7:
Solve the following: 2x/3 = 18
Answer:
Given, 2x/3 = 18
=> 2x = 3 * 18
=> 2x = 54
=> x = 54/2
=> x = 27
Question 8:
Solve the following: 1.6 = y/1.5
Answer:
Given, 1.6 = y/1.5
=> y = 1.6 * 1.5
=> y = 2.40
Question 9:
Solve the following: 7x – 9 = 16
Answer:
Given, 7x – 9 = 16
=> 7x = 16 + 9
=> 7x = 25
=> x = 25/7
Question 10:
Solve the following: 14y – 8 = 13
Answer:
Given, 14y – 8 = 13
=> 14y = 13 + 8
=> 14y = 21
=> y = 21/14
=> y = 3/2 [21 and 14 are divided by 7]
Question 11:
Solve the following: 17 + 6p = 9
Answer:
Given, 17 + 6p = 9
=> 6p = 9 – 17
=> 6p = -8
=> p = -8/6
=> p = -4/3 [8 and 6 are divided 2]
Question 12:
Solve the following: x/3 + 1 = 7/15
Answer:
Given, x/3 + 1 = 7/15
=> x/3 = 7/15 – 1
=> x/3 = (7 - 15)/15 [LCM (15, 1) = 15]
=> x/3 = -8/15
=> x = 3 * (-8/15)
=> x = (-3 * 8)/15
=> x = -24/15
=> x = -8/5 [24 and 15 are divided by 3]
Exercise 2.2
Question 1:
If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number?
Answer:
Let the number be x.
According to question,
(1/2) * (x – 1/2) = 1/8
=> (x – 1/2) = (1/8) * (2/1)
=> x – 1/2 = 2/8
=> x -1/2 = 1/4
=> x = 1/4 + 1/2
=> x = (1 + 2)/4
=> x = 3/4
Hence, the number is 3/4
Question 2:
The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and breadth?
Answer:
Let the breadth of the pool be x m.
Then, the length of the pool = 2x + 2 m
Perimeter = 2(l + b)
=> 154 = 2(2x + 2 + x)
=> 154 =2(3x + 2)
=> 154 = 6x + 4
=> 6x = 154 – 4
=> 6x = 150
=> x = 150/6
=> x = 25
Length of the pool = 2x + 2 = 2 * 25 + 2 = 50 + 2 = 52 m
Breadth of the pool = 25 m
Hence, the length of the pool is 52 m and breadth is 25 m
Question 3:
The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4 cm. What is the length of either of the remaining equal sides?
Answer:
Let each of equal sides of an isosceles triangle be x cm.
Perimeter of a triangle = Sum of all three sides
=> 4 = 4/3 + x + x
=> 2x + 4/3 = 62/15
=> 2x = 62/15 – 4/3
=> 2x = (62 * 1 – 4 * 5)/15
=> 2x = (62 - 20)/15
=> 2x = 42/15
=> x = 42/(15 * 2) => x = 42/30 => x = 14/10
=> x = 1cm.
Hence, each equal side of an isosceles triangle is 1 cm.
Question 4:
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Answer:
Sum of two number = 95
Let the first number be x.
Then, another number be x +15.
According to the question,
x + x + 15 = 95
=> 2x + 15 = 95
=> 2x = 95 – 15
=> 2x = 80
=> x = 80/2
=> x = 40
So, the first number = 40
Another number = 40 + 15 = 55
Hence, the two numbers are 40 and 55
Question 5:
Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
Answer:
Let the two numbers be 5x and 3x
According to question,
5x – 3x = 18
=> 2x =18
=> x = 18/2
=> x = 9
Hence, first number = 5 * 9 = 45
and, second number = 3 * 9 = 27.
Question 6:
Three consecutive integers add up to 51. What are these integers?
Answer:
Let the three consecutive integers be x x + 1 and x + 2.
According to the question,
x + x + 1 + x + 2 = 51
=> 3x + 3 = 51
=> 3x = 51 – 3
=> 3x = 48
=> x = 48/3
=> x = 16
Hence, first integer = 16, second integer = 16 + 1 = 17 and third integer = 16 + 2 = 18
Question 7:
The sum of three consecutive multiples of 8 is 888. Find the multiples.
Answer:
Let the three consecutive multiples of 8 be x, x + 8 and x +16.
According to question,
x + x + 8 + x + 16 = 888
=> 3x + 24 = 888
=> 3x = 888 – 24
=> 3x = 864
=> x = 864/3
=> x = 288
Hence, first multiple of 8 = 288, second multiple of 8 = 288 + 8 = 296
and third multiple of 8 = 288 + 16 = 304.