Question

3t-2 upon 3+2t+3 upon 2 is equal to t+7 upon 6

Answer 1

Answer:

2/11

Step-by-step explanation:

As per the provided information in the given question, we have :

• $\sf {\dfrac{3t-2}{3} + \dfrac{2t + 3}{2} = \dfrac{t + 7}{6} }$

We've to solve this equation i.e, we have to find out the value of t.

Basically, this question can be solved using the cross-multiplication method and transposition method.

In cross-multiplication method, we cross multiply the values. Here, firstly we'll simplify the L.H.S. In transposition method, we transpose the values from LHS to RHS and vice-versa and changing the arithmetic operator to calculate the value of the unknown value.

$\dashrightarrow \quad \rm {\dfrac{3t-2}{3} + \dfrac{2t + 3}{2} = \dfrac{t + 7}{6} }$

Taking the LCM in LHS and solving further using the fractions rules.

$\dashrightarrow \quad \rm { \dfrac{2(3t - 2) + 3(2t + 3)}{6} = \dfrac{t + 7}{6} }$

Performing multiplication using the multiplication over addition property.

$\dashrightarrow \quad \rm { \dfrac{6t - 4 + 6t + 9}{6} = \dfrac{t + 7}{6} }$

Combining the like terms in the numerator of the LHS.

$\dashrightarrow \quad \rm { \dfrac{12t + 5}{6} = \dfrac{t + 7}{6} }$

Performing cross multiplication.

$\dashrightarrow \quad \rm { 6(12t + 5) = 6(t + 7)}$

Once again, performing multiplication using the multiplication over addition property as we did in the earlier step.

$\dashrightarrow \quad \rm { 72t + 30 = 6t + 42 }$

Transposing the like terms from LHS to RHS and vice-versa.

$\dashrightarrow \quad \rm { 72t - 6t= 42 - 30}$

Performing subtraction in both sides.

$\dashrightarrow \quad \rm { 66t= 12}$

Now, transposing 66 from LHS to RHS.

$\dashrightarrow \quad \rm { t=\cancel{ \dfrac{ 12}{66}}}$

$\dashrightarrow \quad \underline{\boxed{\bf{ t = \dfrac{2}{11} }}}$

Therefore, the value of t is 2/11.

$\rule{200}2$

Answer 2

$\large{ \bold{ \boxed{ \sf \: given \: \: equation \: \: is \: }}}$

3t-2 upon 3+2t+3 upon 2 is equal to t+7 upon 6

= 3t-2/3 + 2t+3/2 = t+7/6

= 6t-4+6t+9/6= 6t+7/6

Lcm of 6 both sides

= 12t+5/6= 6t+7/6

Multiplying both 6 and 6

6× 12t+5/6 = 6× 6t+7/6

12t + 5 = 6t+7

= 12t-6t = 7-5 ( tranceposing 6t to LHS and 5 to RHS)

6t = 2

t = 2/6

cut 2 and 6

= 1/3 Answer