वैदिक बीजगणित (11) | बीजगणितीय समीकरण |
(भाग 8)
चरण 1
In an equation there is always an equality sign. The equality sign
shows that the value of the expression to the left of the sign (the left hand side or L.H.S.) is equal to the value of the expression to the right of the sign (the right hand side or R.H.S.).
एक समीकरण में, समता या समिका या बराबर का चिन्ह सदैव होता है। समता का चिन्ह यह दर्शाता है कि इस चिन्ह के बाईं ओर के व्यंजक ‘बायाँ पक्ष’ या (LHS) का मान चिन्ह के दाईं ओर के व्यंजक ‘दायाँ पक्ष’ या (RHS) के मान के बराबर है।
Equation:- An equation is a condition on a variable such that two expressions in the variable should have equal value.
OR
In short, an equation is a condition on a variable. The condition is
that two expressions should have equal value. Note that at least
one of the two expressions must contain the variable.
Roll No. 04 : - An equation remains the same, when the expression
on the left and on the right are interchanged. This property is often
useful in solving equations.
An equation remains the same if the L.H.S. and the R.H.S. are interchanged.
01. Write the following statements in the form of equations:
01. The sum of three times x and 11 is 32.
02. If you subtract 5 from 6 times a number, you get 7.
03. One fourth of m is 3 more than 7.
04. One third of a number plus 5 is 8.
02. Write equations for the following statements:
निम्न के लिए समीकरण लिखिए।
01. The sum of numbers x and 4 is 9.
02. The difference between y and 2 is 8.
03. Ten times a is 70
04. The number b divided by 5 gives 6.
05. Three fourth of t is 15. (vi) Seven times m plus 7 gets you
77.
06. One fourth of a number minus 4 gives 4.
07. If you take away 6 from 6 times y, you get 60.
08. If you add 3 to one third of z, you get 30.
03. Convert the following equations in statement form:
01. p + 4 = 15
02. m – 7 = 3
03. 2m = 14
04. 2m = 14
05. m/6 = 3
06. 3m/6 = 6
07. 3p + 4 = 25
08. 4p – 2 = 18
09. p/2 + 2 = 8
10. p/2 – 2 = 8
10. Solve the following:
10. निम्न को सरल कीजिए।
01 6x = 18
02 7y = 14
03 2x = 6
04 4m = 16
05 2x/ 3 = 6
06 y/6 = 7
07 y/8 = 4
08 x + 4 = 13
09 x + 5 = 18
10 y – 5 = 7
11 x + 10 = 12
12 x – 10 = 14
13 7y – 10 = 0
14 4y – 16 = 0
15 5m – 25 = 0
16 5m + 25 = 0
17 3x + 9 = 0
18 2x – 6 = 0
11. Solve the following:
11. निम्न को सरल कीजिए।
01. 2m + 4 = 8
02. 4m – 5 = 11
03. 11 + 2a = 25
04. 12x + 4 = 3x
05. 75 – 3a =35
06. 2x – 3 = 5
07. 7 – 4 y = 3
08. 20 x = x + 95
09. x/2 + 5 = 10
10. x/8+6 = 8
05. 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.
12. 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
13. Give first the step you will use to separate the variable and
then solve the equation:
(a) 3l = 42
(b) b/2 = 8
(c) p/7 = 4
(d) 4x = 25
(e) 8y = 36
(f) z/3 = 5 /4
(g) a /5 = 7/15
(h) 20t = – 10
15. Solve the following equations:
16. Solve the following equations.
17. Solve the following equations:
01. 2(x + 4) = 12
02. 3(n – 5) = 21
03. 3(n – 5) = – 21
04. 3 – 2(2 – y ) = 7
05. – 4(2 – x) = 9
06. 4(2 – x) = 9
07. 4 + 5 (p – 1) = 34
08. 34 – 5(p – 1) = 4
18. Solve the following equations:
01. 4 = 5(p – 2)
02. – 4 = 5(p – 2)
03. –16 = –5 (2 – p)
04. 10 = 4 + 3(t + 2)
05. 28 = 4 + 3(t + 5)
06. 0 = 16 + 4(m – 6)
07. 5 (3 – x) = 10
08. 3 (2 + x) = 12
09. 3 (x + 2) = 2
10. 3y + 7 = 5 – y
11. 8y – 3 = – 2y – 3
12. 6y – 7 = 2 (y + 3)
13. 10 (x + 2) = 5 (x – 3)
14. 3 (x + 1) = x + 5
19. Solve the following equations:
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