Page 113 - Start Up Mathematics_7

contd...
Whether the equation
S. No. Equation Value
is satisfied (Yes/No)
(iii) 3x = 12 x = 4 Yes
(iv) 2y + 3 = 9 y = –3 No
y
(v) = 3 y = 6 Yes
2
(vi) 3m – 2 = 16 m = 6 Yes

Example 2: Check whether the value given in the brackets is the solution to the given equation
or not:
n
(a) 2y + 3 = 21; (y = –9) (b) 6 – 3p = 0; (p = 2) (c) – 4 = –2; (n = 6)
3
Solution: (a) On putting y = –9, LHS = 2(–9) + 3 = –15 ≠ 21 = RHS
∴ y = –9 is not the solution of the given equation.
(b) On putting p = 2, LHS = 6 – 3p = 6 –3(2) = 0 = RHS
∴ p = 2 is the solution of the given equation.
n 6
(c) On putting n = 6, LHS = – 4 = – 4 = –2 = RHS
3 3
∴ n = 6 is the solution of the given equation.
Example 3: Write equations for the following statements:

(a) The sum of x and 7 is 12. (b) One more than twice p is 8.
(c) Seven times m plus 7 gives 77. (d) Two less than three-fourth of t is 15.
(e) If you take away 5 from 5 times y, you get 20.

Solution: (a) x + 7 = 12 (b) 2p + 1 = 8 (c) 7m + 7 = 77
3
(d) t – 2 = 15 (e) 5y – 5 = 20
4
Example 4: Write the following equations in statement forms:
3m
(a) p + 3 = 12 (b) 3p + 4 = 26 (c) = 6
q 5
(d) 5p – 2 = 18 (e) + 2 = 2
2
Solution: (a) The sum of numbers p and 3 is 12. (b) Four added to three times p gives 26.
(c) Three-fifth of a number is 6. (d) Five times p minus 2 gives 18.
(e) 2 added to half of q gives 2.

Example 5: Set up an equation in the following cases:
(a) Imran says that he has 3 marbles less than four times the marbles Rohit has.
Imran has 29 marbles.
(b) The teacher tells the class that the highest marks obtained by a student in
her class is 2 less than thrice the lowest marks. The highest score is 85.

(c) Garima’s father is 43 years old. He is 19 years older than
twice the Garima’s age.
(d) In a right-angled triangle, one of the angles is twice the
other. (Take smaller of the two acute angles as a degrees.)

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