Question

Solve the equation : x/3 + x/4 = 63​

Answer 1

Answer:

Question :

${\implies{\sf{\dfrac{x}{3} + \dfrac{x}{4} = 63}}}$

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

Solution :

${\implies{\sf{\dfrac{x}{3} + \dfrac{x}{4} = 63}}}$

Taking the LCM of denominators.

${\implies{\sf{\dfrac{(x \times 4) + (x \times 3)}{12} = 63}}}$

${\implies{\sf{\dfrac{4x+3x}{12} = 63}}}$

${\implies{\sf{\dfrac{7x}{12} = 63}}}$

${\implies{\sf{x = 63 \times \dfrac{12}{7}}}}$

${\implies{\sf{x = \cancel{63} \times \dfrac{12}{\cancel{7}}}}}$

${\implies{\sf{x = 9 \times 12}}}$

${\implies{\sf{x = 108}}}$

${\bigstar{\underline{\boxed{\textbf{\textsf{\red{x = 108}}}}}}}$

Hence, the value of x is 108.

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

Verification :

${\implies{\sf{\dfrac{x}{3} + \dfrac{x}{4} = 63}}}$

Substituting the value of x.

${\implies{\sf{\dfrac{108}{3} + \dfrac{108}{4} = 63}}}$

${\implies{\sf{ \cancel{\dfrac{108}{3}} + \cancel{\dfrac{108}{4}} = 63}}}$

${\implies{\sf{36+27= 63}}}$

${\implies{\sf{63= 63}}}$

${\bigstar{\underline{\boxed{\textbf{\textsf{\red{LHS = RHS}}}}}}}$

Hence Verified!

$\overline{\rule{220pt}{2.5pt}}$

Learn More :

☼ Algebraic identities:-

• ➛ (a+b)²+(a-b)² = 2a²+2b²
• ➛ (a+b)²-(a-b)² = 4ab
• ➛ (a+b)(a -b) = a²-b²
• ➛ (a+b+c)² = a²+b²+c²+2ab+2bc+2ca
• ➛ (a-b)³ = a³-b³-3ab(a-b)
• ➛ (a³+b³) = (a+b)(a²-ab+b²)
• ➛ a²+b² = (a+b)²-2ab
• ➛ a³-b³ = (a-b)(a²+ab +b²)
• ➛ If a + b + c = 0 then a³ + b³ + c³ = 3abc

☼ 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 ( )

☼ EXPONENT :

↝ The exponent of a number says how many times to use the number in a multiplication.

☼ LAW OF EXPONENT :

The important laws of exponents are given below:

• ➠ ${\rm{{a}^{m} \times {a}^{n} = {a}^{m + n}}}$
• ➠ ${\rm{{a}^{m}/{a}^{n} = {a}^{m - n}}}$
• ➠ ${\rm{({a}^{m})^{n} = {a}^{mn}}}$
• ➠ ${\rm{{a}^{n}/{b}^{n} = ({a/b})^{n} }}$
• ➠ ${\rm{{a}^{0} = 1}}$
• ➠ ${\rm{{a}^{ - m} = {1/a}^{m}}}$
• ➠ ${\rm{{a}^{\frac{1}{n} } = \sqrt[n]{a}}}$

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Answer 2

As per the data given in the question,

We have to determine the value of "x" by using the expression given in the question.

As per question,

It is given that,

$\frac{x}{3} +\frac{x}{4} = 63$

For finding the value of "x" we will first solve the LHS side and then by using cross multiplication we will determine the value of "x".

So, we will get it as,

$\frac{x}{3} +\frac{x}{4} = 63\\=>\frac{4x+3x}{12}=63\\=>\frac{7x}{12} = 63\\=>7x=63\times 12\\=>x = \frac{63\times 12}{7}\\=>x = 108$

Hence, value of "x" in the given equation will be 108.