Question

if the difference of 8 times the number and 6 is same as the sum of four time the number and 14 then find the number ​

Answer 1

${{\underline{\underline{{\textsf{\textbf{Answer : }}}}}}}$

➡ The number is 5 ☑

${{\underline{\underline{{\textsf{\textbf{Explanation : }}}}}}}$

Given statements :

• The difference of 8 times a number and 6 is same as the sum of four times the number and 14

Step 1:

If we assume the number as $x$

The statement goes like this :

• (8 times $x$) - 6 is equal to (4 times $x$) + 14

Step 2:

The equation forms :

➙ 8x - 6 = 4x + 14

Step 3:

〄 Solving for x :

➪ 8x - 6 = 4x + 14

➪ 8x - 4x = 14 + 6

[ Transposing 4x to R. H. S. and 6 to L. H. S. ]

➪ 4x = 20

➪ x = $\sf{\cancel{\frac{20}{5}}}$

➪ x = 5

${{\underline{\underline{{\textsf{\textbf{Finally,}}}}}}}$

➡ The number is 5 ☑

${{\underline{\underline{{\textsf{\textbf{Verification : }}}}}}}$

Substitute $x$in the equation :

➔ 8(5) - 6 = 4(5) + 14

➔ 40 - 6 = 20 + 14

➔ 34 = 34

Therefore, L. H. S. = R. H. S.

${{\underline{\underline{{\textsf{\textbf{Hence, Verified: }}}}}}}$

Answer 2

Answer:

Question:-

• If the difference of 8 times the number and 6 is same as the sum of four times the number and 14, then find the number.

$\bf\underbrace\orange{Answer:}$

Given :-

• The difference of 8 times the number and 6 is same as the sum of four times the number and 14.

To Find :-

• The number.

$\bf\underbrace\orange{Solution:}$

Let the required number be x.

Case - 1 :-

So, Difference of 8 times the number and 6 means

$\bf \implies \:8x - 6$

Case - 2 :-

And, sum of 4 times the number and 14 means

$\bf\implies \:4x + 14$

According to statement,

The difference of 8 times the number and 6 = The sum of four time the number and 14.

$\bf\implies \:8x - 6 = 4x + 14$

On transposition, we get

$\bf\implies \:8x - 4x = 14 + 6$

$\bf\implies \:4x = 20$

$\bf\implies \:x = 5$

____________________________________________

$\bf\underbrace\orange{Verification:}$

The difference of 8 times the number and 6

= 8x - 6

= 8 × 5 - 6

= 40 - 6

= 34

Sum of 4 times the number and 14

= 4x + 14

= 4 × 5 + 14

= 20 + 14

= 34

⇛ The difference of 8 times the number and 6 is same as the sum of four times the number and 14.

$\bf \: Hence, \: Verified.$