Question

18%7D%20" id="TexFormula1" title=" \frac{3}{2} + \frac{2m}{9} = \frac{37}{18} " alt=" \frac{3}{2} + \frac{2m}{9} = \frac{37}{18} " align="absmiddle" class="latex-formula">
How do I solve this and make it the most simplified it can be?​

Answer 1

Answer:

$m = \frac{5}{2}$

Step-by-step explanation:

$\frac{3}{2} + \frac{2m}{9} = \frac{37}{18}$

Multiply through by 18 to eliminate the fraction

That's

$18 \times \frac{3}{2} + 18 \times \frac{2m}{9} = 18 \times \frac{37}{18} \\ 27 + 4m = 37$

Subtract 27 from both sides

That's

$27 - 27 + 4m = 37 - 27 \\ 4m = 10$

Divide both sides by 4

That's

$\frac{4m}{4} = \frac{10}{4}$

We have the final answer as

$m = \frac{5}{2}$

Hope this helps you

Answer 2

➢ Answєr :

$\Huge{\boxed{\sf{\red{m = \frac{5}{2}}}}}$

➢ Explαnαtion :

$\displaystyle{\sf{ \frac{3}{2} + \frac{2m}{9} = \frac{37}{18}}}$

| ∵ Transposing 3/2 to R.H.S

$\implies$ $\displaystyle{\sf{ \frac{2m}{9} = \frac{37}{18} - \frac{3}{2}}}$

$\implies$ $\displaystyle{\sf{ \frac{2m}{9} = \frac{37-27}{18}}}$

$\implies$ $\displaystyle{\sf{ \frac{2m}{9} = \frac{10}{18} = \frac{5}{9}}}$

$\implies$ $\displaystyle{\sf{ 2m = \frac{5}{9} \times 9}}$

$\implies$ $\displaystyle{\sf{ 2m = 5}}$

$\longrightarrow$ $\large{\boxed{\sf{\red{ m = \frac{5}{2}}}}}$