To combine rational numbers, first we have to check whether the denominators are same or not.
(i) If the denominators are same, we can put one denominator and combine the numerators.
(ii) If the denominators are not same, we will take least common multiple and combine the numerators.
(iii) Keep the unknowns in one side of the equal sign.
(iv) Do the possible simplification and get the value of unknown.
Problem 1 :
Solve:
x/2 + x/4 + x/5 + 10000 = x
Solution :
x/2 + x/4 + x/5 + 10000 = x
10000 = x/2 - x/4 - x/5
LCM of 2, 4, 5 is 20.
10000 = (20x-10x-5x-4x)/20
10000 = (20x-19x)/20
10000 = x/20
x/20 = 10000/1
Cross multiplying both sides.
x∙1 = 20∙10000
x = 200000
So, the answer is x = 200000.
Problem 2 :
If (5x/3) - 4 = 2x/5, then the numerical value of 2x-7 is
Solution :
(5x/3) - 4= 2x/5
Find common denominator
(5x - 12)/3= 2x/5
Doing cross multiplication.
5(5x-12) = 6x
25x-60 = 6x
25x-6x = 60
19x = 60
x = 60/19
The numerical value of 2x - 7= 2(60/19) - 7
= (120/19) - 7
=
-13/19
Problem 3 :
-4/3y = -3/4 then y =
Solution:
Given, -4/3y = -3/4
y = (-3/4)×(-3/4)
y = (3/4)²
Hence, the value of y is (3/4)².
Problem 4 :
(x/5) + 30 = 18 has the solution as
Solution :
Transposing 30 to RHS and it becomes -30.
x/5 = 18-30
x/5 = -12
x = -12×5
x = -60
So, the solution as x = -60.
Problem 5 :
If (2/5) (x-2) = 5-(3/5)x then x = ?
Solution :
(2/5)(x-2)= 5 - (3/5)x
(2x-4) / 5 = (25-3x) / 5
Multiplying by 5 on both sides, we get
2x-4 = 25-3x
2x+3x = 25+4
5x = 29
x = 29/5
So, the answer is x = 29/5.
Problem 6 :
x/5 = (x - 1)/6
Solution :
Doing cross multiplication.
6x= 5(x-1)
6x= 5x-5
6x-5x = -5
x = -5
So, the answer is x= -5.
Problem 7:
(x/2) - (1/4) (x-1/3) = (1/6) (x+1) + (1/12)
Solution :
(x/2) - (1/4) (x-1/3) = (1/6) (x+1) + (1/12)
Combine like terms.
x/2 - x/4 + 1/12 = 1/6x + 1/6 + 1/12
LCM of 2, 4, 12 is 12 and LCM of 6, 6, 12 is 12.
(6x - 3x + 1)/12 = (2x + 2 + 1)/12
Simplify like terms.
(3x+1) / 12 = (2x+3) / 12
Multiplying by 12 on both sides, we get
3x + 1 = 2x + 3
3x - 2x = 3 - 1
x = 2
So, the answer is x = 2.
Problem 8 :
(1/2) (x + 1) + (1/3) (x - 1) = (5/12) (x - 2)
Solution :
Least common multiple of 2, 3, and 12 is 12.
[6(x + 1) + 4(x - 1)] / 12 = 5(x-2) / 12
Multiplying by 12 on both sides.
6(x + 1) + 4(x - 1) = 5(x-2)
Using distributive property.
6x + 6 + 4x - 4 = 5x - 10
10x + 2 = 5x - 10
5x = -10 - 2
x = -12/5
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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