Question

solve the following linear equation for the unknown variable and verify the solution
3x-12/4=30-2x

Answer 1

3x-12/4=30-2x

=3X-12=4[30-2x]

=3x-12=120-8x

=11x=132

=x=132/11

=12

Answer 2

Solution ;

$\mathsf{ \frac{3x - 12}{4} = 30 - 2x } \\ \\ \bold{on \: cross \: multiplying..} \\ \\ \mathsf{3x - 12 = 4(30 - 2x)} \\ \\ \mathsf{3x - 12 =120 - 8x} \\ \\ \mathsf{3x + 8x = 120 + 12} \\ \\ \mathsf{11x = 132} \\ \\ \mathsf{x = \frac{132}{11} } \\ \\ \boxed{ \bold{x = 12}}$

Verification :

Putting the value of x in the given equation ;

$\mathsf{ \frac{3x - 12}{4} = 30 - 2x} \\ \\ \mathsf{ \frac{3(12) - 12}{4} = 30 - 2(12)} \\ \\ \mathsf{ \frac{36 - 12}{4} = 30 - 24} \\ \\ \mathsf{ \frac{24}{4} = 6} \\ \\ \mathsf{\implies {6 = 6} } \\ \\ \therefore \underline{ \bold{ LHS = RHS}}$

Hence, the value of x is 12.