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Solve the equation and show all your work.
3(x- 5) = 6

Sagot :

AadhPrit

Answer:

x = 7

Step-by-step explanation:

CONCEPT :

Here, we will use the below following steps to find a solution using the transposition method:

  • Step 1 :- we will Identify the variables and constants in the given simple equation.
  • Step 2 :- then we Simplify the equation in LHS and RHS.
  • Step 3 :- Transpose or shift the term on the other side to solve the equation further simplest.
  • Step 4 :- Simplify the equation using arithmetic operation as required that is mentioned in rule 1 or rule 2 of linear equations.
  • Step 5 :- Then the result will be the solution for the given linear equation.

[tex]\begin{gathered}\end{gathered}[/tex]

SOLUTION :

To solve this equation, we'll use this given concept :

[tex]\begin{gathered} \qquad{\twoheadrightarrow{\sf{3(x - 5) = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{(3 \times x) - (3 \times 5) = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{(3x) - (15) = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{3x - 15 = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{3x = 6 + 15}}}\\\\\qquad{\twoheadrightarrow{\sf{3x =21}}}\\\\\qquad{\twoheadrightarrow{\sf{x = \dfrac{21}{3}}}}\\\\\qquad{\twoheadrightarrow{\sf{x = 7}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{x = 7}}}}}}\end{gathered}[/tex]

Hence, the value of x is 7.

[tex]\rule{300}{2.5}[/tex]

TheAmethyst

Hey ! there

Answer:

  • x = 7

Step-by-step explanation:

In the question we are given with an equation that is 3 ( x - 5 ) = 6 . And we're asked to solve the equation that means we have to find the value of x .

Solution : -

[tex] \dashrightarrow \qquad \: 3(x - 5) = 6[/tex]

Step 1 : Solving parenthesis by using distributive property that means multiplying 3 with x as well as - 5 :

[tex] \dashrightarrow \qquad \: (3 \times x) - (3 \times 5) = 6[/tex]

Simplifying it ,

[tex] \dashrightarrow \qquad \: 3x - 15 = 6[/tex]

Step 2 : Adding 15 to both sides :

[tex] \dashrightarrow \qquad \: 3x - \cancel{15 }+ \cancel{15 }= 6+ 15[/tex]

On cancelling -15 with 15 , We get :

[tex] \dashrightarrow \qquad \: 3x = 6 + 15[/tex]

Step 3 : Adding 6 and 15 :

[tex] \dashrightarrow \qquad \: 3x = 21[/tex]

Step 4 : Now to make our variable isolate , dividing with 3 on both sides :

[tex] \dashrightarrow \qquad \: \dfrac{ \cancel{3}x}{ \cancel{3}}= \cancel{\dfrac{21}{3} }[/tex]

On further calculations , We get ,

[tex] \dashrightarrow \qquad \: \purple{ \underline{\boxed{\frak{ x = 7}}}} \quad \star[/tex]

  • Henceforth , value of x is 7 .

Verifying : -

Atlast , we are checking our answer by substituting the above value of x in given equation . So ,

  • 3 ( x - 5 ) = 6

  • 3 ( 7 - 5 ) = 6

  • 3 ( 2 ) = 6

  • 6 = 6

  • L.H.S = R.H.S

  • Hence , Verified .

Therefore , our solution is correct .

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