Question

Which value of $“d”$ makes the following linear equation true?
$6(d-4)=12$

Answer 1

Detailed step-by-step solution:
A linear equation is an algebraic equation consisting of one or more variables, where each term is either a constant or a variable raised to the first power.
If a linear equation has a solution
$x=a,$ then $x=a$ will satisfy the linear equation.

Solving for d in $6(d-4)=12$ to make the equation true means L.H.S. $=$ R.H.S.
$6(d-4)=12$
$(6\times d-6\times 4)=12$ (using distributive property)
$6d-24=12$ (solving bracket)
$6d=12+24$ (transposing 24 to right)
$6d=36$ (dividing 6 on both sides)
$d=6$

Value of $d=6$
Now, let’s check if putting the value of $d$ in the given equation makes the linear equation true or not.
$6(d-4)=12$
$6(6-4)=12$ (solving the bracket)
$6\left(2\right)=12$
$12=12$
$LHS=RHS$
Hence proved
For the value of $d=6,$ the linear equation is true.

So, option D is the correct answer.