Question

Solve for x: (x/2) + (x/3) + (x/4) = 26​

Answer 1

Question:-

Solve for x

$\frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 26$

Solution:-

2×3× 4 is 24

So, by adding all we get

$\frac{12x + 8x + 6x}{24} = 26$

$\frac{26x}{24} = 26$

$26x = 26 \times 24$

$x = \frac{26 \times 24}{26}$

$x = 24$

Final answer:-

The value of x is 24

Answer 2

Required Solution :

Here, we are given a linear equation. We have to find the value of x i.e, solve for x. We'll use transposition method to find the value of x.

★ Transposition method :

➝ This is the method used to solve a linear equation having variables and constants.

➝ In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

Explication of steps :

$\longrightarrow \sf { \dfrac{x}{2} + \dfrac{x}{3} + \dfrac{x}{4} = 26}$

➝ L.C.M of 2,3,4 is 12. Writing it into the denominator in L.H.S.

$\longrightarrow \sf { \dfrac{6x + 4x + 3x}{12} = 26}$

➝ Simplifying further and adding the numbers in the numerator in L.H.S.

$\longrightarrow \sf { \dfrac{13x}{12} = 26}$

➝ Now, transposing 12 from L.H.S to R.H.S. Since it is in the form of division in L.H.S, it will become in the form of multiplication in R.H.S.

$\longrightarrow \sf { 13x= 26 \times 12}$

➝ Multiplying 26 with 12.

$\longrightarrow \sf { 13x= 312}$

➝ Now, transposing 13 from L.H.S to R.H.S. Since it is in the form of multiplication in L.H.S, it will become in the form of division in R.H.S.

$\longrightarrow \sf { x= \cancel{\dfrac{312}{13}}}$

➝ Dividing 312 by 13.

$\longrightarrow\underline{ \boxed{\sf { x= 24}}}\; \bigstar$

Therefore, value of x is 24.