Mark the statement as true or false. The solution of 3(k – 1) = 2(2 + k) is k = 7. About the author Eden

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! ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 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! Reply

Statement is true

finding k

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

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

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

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

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

Hence,thegivenstatementistrue!–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––VERIFICATION:–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]

Substitutingthevalueofk,[tex] \leadsto\rm 3 (7 – 1) [/tex]

Removingthebrackets,[tex] \leadsto\rm 21 – 3 [/tex]

Subtracting3from21,[tex] \leadsto\rm 18 [/tex]

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

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

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

Adding14to4,[tex] \leadsto\rm 18 [/tex]

———————————————————–LHS = RHS.

Hence verified!