Question

0.5x + x/3=0.25x+7?​

Answer 1

Answer:

Qᴜᴇsᴛɪᴏɴ :

$\dashrightarrow{\sf{{0.5x} + \dfrac{x}{3} = {0.25x} + 7}}$

$\begin{gathered}\end{gathered}$

Sᴏʟᴜᴛɪᴏɴ :

$\dashrightarrow{\sf{\dfrac{5x}{10} + \dfrac{x}{3} = {\dfrac{25x}{100} } + 7}}$

$\dashrightarrow{\sf{ \cancel{\dfrac{5x}{10}} + \dfrac{x}{3} = {\cancel{\dfrac{25x}{100}}} + 7}}$

$\dashrightarrow{\sf{{\dfrac{x}{2}} + \dfrac{x}{3} = {\dfrac{x}{4}} + 7}}$

Taking x/4 to L.H.S,

$\dashrightarrow{\sf{{\dfrac{x}{2}} + \dfrac{x}{3} - {\dfrac{x}{4}} = 7}}$

Taking LCM,

$\dashrightarrow{\sf{{\dfrac{(x \times 6) + (x \times 4) - (x \times 3)}{12}} = 7}}$

$\dashrightarrow{\sf{{\dfrac{6x + 4x-3x}{12}} = 7}}$

$\dashrightarrow{\sf{{\dfrac{10x-3x}{12}} = 7}}$

$\dashrightarrow{\sf{{\dfrac{7x}{12}} = 7}}$

Multiplying both side by 12

$\dashrightarrow{\sf{{\dfrac{7x}{12} \times 12} = 7 \times 12}}$

$\dashrightarrow{\sf{{\dfrac{7x}{\cancel{12}} \times \cancel{12}} = 84}}$

$\dashrightarrow{\sf{7x = 84}}$

Taking L.H.S to R.H.S

$\dashrightarrow{\sf{x = \dfrac{84}{7} }}$

$\dashrightarrow{\sf{x = \cancel{\dfrac{84}{7}}}}$

$\dashrightarrow{\sf{x = 12}}$

$\dashrightarrow{\underline{\underline{\sf{x = 12}}}}$

$\longrightarrow{\underline{\boxed{\sf{\pink{x = 12}}}}}$

∴ The value of x is 12.

$\begin{gathered}\end{gathered}$

Vᴇʀɪғɪᴄᴀᴛɪᴏɴ :

$\dashrightarrow{\sf{{0.5x} + \dfrac{x}{3} = {0.25} + 7}}$

Putting value of (x = 12)

$\dashrightarrow{\sf{{0.5 \times 12} + \dfrac{12}{3} = {0.25 \times 12} + 7}}$

$\dashrightarrow{\sf{{6} + \dfrac{12}{3} = {3} + 7}}$

$\dashrightarrow{\sf{{6} + \dfrac{12}{3} = 10}}$

Taking LCM of 6 + 12/3.

$\dashrightarrow{\sf{\dfrac{(6 \times 3 ) + (12 \times 1)}{3} = 10}}$

$\dashrightarrow{\sf{\dfrac{18 +12}{3} = 10}}$

$\dashrightarrow{\sf{\dfrac{30}{3} = 10}}$

$\dashrightarrow{\sf{ \cancel{\dfrac{30}{3}} = 10}}$

$\dashrightarrow{\underline{\underline{\sf{10 = 10}}}}$

$\longrightarrow{\underline{\boxed{\sf{\pink{LHS= RHS}}}}}$

∴ Hence Verified!

$\begin{gathered}\end{gathered}$

Lᴇᴀʀɴ Mᴏʀᴇ :

☼ BODMAS :

BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.

It stands for :-

• ↠ B - Brackets,
• ↠ O - Order of powers or roots,
• ↠ D - Division,
• ↠ M - Multiplication 
• ↠ A - Addition,
• ↠ S - Subtraction.

It means that expressions having multiple operators need to be simplified from left to right in this order only.

☼ BODMAS RULE :

First, we solve brackets, then powers or roots, then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.

• ↠ Addition (+)
• ↠ Subtraction (-)
• ↠ Multiplication (×)
• ↠ Division (÷)
• ↠ Brackets ( )

$\begin{gathered}\end{gathered}$

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