Solve each of the following equations. Also, verify the result in each case.
5.
5x-4 - x-3 = x+6
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8 5 4
Answers
Question 1:
x - 2 = 7
Solution:
Given, x – 2 = 7
By adding 2 to both sides, we get
x – 2 + 2 = 7 + 2
⇒ x = 7 + 2
⇒ x = 9
Question 2:
y + 3 = 10
Solution:
Given,y + 3 = 10
By subtracting 3 from both sides, we get
y + 3 – 3 = 10 – 3
⇒ y = 10 – 3
⇒ y = 7
Question 3:
6 = z + 2
Solution:
Given,6 = z + 2
By substracting 2 from both sides, we get
6 – 2 = z + 2 – 2
⇒4 = z + 2 – 2
⇒ 4 = z
⇒ z = 4
Question 4:
Solution:
Given,
By subtracting from both sides, we get
Question 5:
6x = 12
Solution:
Given,6x = 12
After dividing both sides by 6, we get
Question 6:
Solution:
Given,
After multiplying both sides by 5, we get
Question 7:
Solution:
Given,
By multiplying both sides with 3, we get
After dividing both sides by 2, we get
Question 8:
Solution:
Given,
After multiplying both sides by 1.5, we get
Question 9:
7x – 9 = 16
Solution:
Given,7x – 9 = 16
By adding 9 to both sides, we get
After dividing both sides by 7, we get
Question 10:
Solution:
Given,14y – 18 = 13
By adding 8 to both sides, we get
14y – 8 + 8 = 13 + 8
⇒ 14y = 21
After dividing both sides by 14, we get
Question 11:
17 + 6p = 9
Solution:
Given, 17 + 6p = 9
After subtracting 17 from both sides, we get
17 + 6p – 17 = 9 – 17
⇒ 6p = –8
After dividing both sides by 6, we get
Question 12:
Solution:
Given,
By transposing 1 from LHS to RHS, we get
After multiplying both sides with 3, we get
Exercise 2.2
Question 1:
If you subtract from a number and multiply the result by , you get . What is the number?
Solution:
Let the number is m.
As per question we have
After dividing both sides by we get
By transposing to RHS, we get
Question 2:
The perimeter of a rectangular swimming pool is 154m. Its length is 2m more than twice its breadth.
What are the length and the breadth of the pool?
Solution:
Given, perimeter of the rectangular swimming pool = 154m
Length is 2 metre more than the breadth.
Let the breadth of the swimming pool = a metre
Therefore, as per question, length of the swimming pool = (2a + 2) metre
We know that,
perimeter of rectangle = 2 (length + breadth)
Therefore, 154m = 2[(2a + 2) + a]
⇒ 154m = 2(2a + 2 + a )
⇒ 154m = 2 (3a + 2)
⇒ 154m = 6a + 4
By subtracting 4 from both sides, we get
154m – 4 = 6a + 4 – 4
⇒ 150m = 6a
After dividing both sides by 6, we get
Since, length = (2a + 2)m
Therefore, by substituting the value of breadth (a), we get
(2 x 25 + 2)m= (50 + 2)m = 52m
Thus, length of the given pool = 52m
And breadth = 25m
The base of an isosceles triangle is The perimeter of the triangle is What is the length of either of the remaining equal sides?
Solution:
Given, Base of the isosceles triangle
Isosceles triangles have two sides equal.
We know that perimeter of an isosceles triangle
= Sum of two equal sides + third side
Let the length of equal sides of the given isosceles triangle = a
And length of unequal side = b
Therefore, perimeter = 2a + b
Therefore,
By subtracting from both sides, we get