Mark the statement as true or false.

The solution of 3(k – 1) = 2(2 + k) is k = 7.​

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1. Statement is true

   finding k

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2. Answer :–

   • The statement is true.

   • The solution of 3 (k – 1) = 2 (2 + k) is 7.

   To find :–

   • Whether the statement is true or false :-

   [tex] \hookrightarrow [/tex] The solution of 3 (k – 1) = 2 (2 + k) = 7.

   Step-by-step explanation :–

   • To find whether the given statement is true or false, we have to solve the equation first!

   [tex] \leadsto\sf3 \: (k – 1) = 2 \: (2 + k)[/tex]

   Removing the brackets,

   [tex] \leadsto\sf3k – 3 = 4 + 2k[/tex]

   Putting the constant and variable terms on different sides by the method of transposition,

   [tex] \leadsto\sf3k – 2k = 4 + 3[/tex]

   On simplifying,

   [tex] \leadsto\sf k = 7[/tex]

   • The value of k is 7.

   Hence, the given statement is true!

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   V E R I F I C A T I O N :–

   To check our answer, let’s put 7 in the place of k and see whether LHS = RHS.

   LHS

   [tex] \leadsto\rm 3 (k – 1) [/tex]

   Substituting the value of k,

   [tex] \leadsto\rm 3 (7 – 1) [/tex]

   Removing the brackets,

   [tex] \leadsto\rm 21 – 3 [/tex]

   Subtracting 3 from 21,

   [tex] \leadsto\rm 18 [/tex]

   RHS

   [tex] \leadsto\rm 2 (2 + k) [/tex]

   Substituting the value of k,

   [tex] \leadsto\rm 2 (2 + 7) [/tex]

   Removing the brackets,

   [tex] \leadsto\rm 4 + 14 [/tex]

   Adding 14 to 4,

   [tex] \leadsto\rm 18 [/tex]

   ———————————————————–

   LHS = RHS.

   Hence verified!

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