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Given below are some equations and the values of the variables. Are these values the solutions to those equations?

No.EquationValue of the VariableSolution (Yes/No)
i.y – 3 = 11y = 3No
ii.17 = n + 7n = 10
iii.30 = 5xx = 6
iv\(\cfrac{m}{2}\) = 14m = 7

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No.EquationValue of the VariableSolution (Yes/No)
i.y – 3 = 11y = 3No
ii.17 = n + 7n = 10Yes
iii.30 = 5xx = 6Yes
iv\(\cfrac{m}{2}\) = 14m = 7No

 i. y – 3 = 11 

∴ y – 3 + 3 = 11 + 3 

…. (Adding 3 to both sides) 

∴ y + 0 = 14 ∴ y = 14

ii. 17 = n + 7 

∴ 17 – 7 = n + 7 – 7 

…. (Subtracting 7 from both sides) 

∴ 17 + (-7) = n + 7 – 7 

∴ 10 = n 

∴  n = 10

iii. 30 = 5x

\(\therefore\) \(\cfrac{30}{5}\) = \(\cfrac{5x}{5}\)

…. (Dividing both sides by 5) 

∴  6 = 1x 

∴ 6 = x 

∴  x = 6

iv. \(\cfrac{m}{2}\)= 14

\(\cfrac{m}{2}\)× 2 = 14 × 2

…. (Multiplying both sides by 2)

\(\cfrac{m\times2}{2\times1}\) = 28

∴ m = 28

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