Question

solve the linear equation ​

Answer 1

Answer:

Given:-

Solve the linear equation : $\dfrac{1}{2} ( x + 5 ) - \dfrac{1}{3} ( x - 2 ) = 4$.

To Find:

The value of "x".

Note:-

●》Here for finding the value of "x", we will first calculate the fraction terms with bracket ( as per BODMAS method ) and then add or subtract by therr signs and also by taking L.C.M ( if it is necessary ). At last, we will transpose the terms for "x" to be calculated.

●》Transposing - For finding unknown value, known value needs to be transposed from its side to another and also signs are changed. For example - Positive becomes Negative, Multiple becomes Divisional.

●》Equation - it means that two side term calculations should be equal.

Solution:-

$\huge\red{\dfrac{1}{2} ( x + 5 ) - \dfrac{1}{3} ( x - 2 ) = 4}$

$\huge\red{ \ \ \ \ The \ \ value \ \ of \ \ x = ?}$

☆ According to note first point~

▪︎$\dfrac{1}{2} ( x + 5 ) - \dfrac{1}{3} ( x - 2 ) = 4$

▪︎$( \dfrac{1}{2} × x + \dfrac{1}{2} × 5 ) - ( \dfrac{1}{3} × x - \dfrac{1}{3} × 2 ) = 4$

▪︎$( \dfrac{1}{2}x + \dfrac{5}{2} ) - ( \dfrac{1}{3}x - \dfrac{2}{3} ) = 4$

☆ Opening brackets, if their is sign out of bracket it will be multiplied to it~

▪︎$\dfrac{1}{2}x + \dfrac{5}{2} - \dfrac{1}{3}x + \dfrac{2}{3} = 4$

☆ Taking common terms one side~

▪︎$\dfrac{1}{2}x - \dfrac{1}{3}x + \dfrac{5}{2} + \dfrac{2}{3} = 4$

☆ L.C.M of denominators 2 and 3 is = 6~

▪︎$\dfrac{1}{2}x × \dfrac{3}{3} - \dfrac{1}{3}x × \dfrac{2}{2} + \dfrac{5}{2} × \dfrac{3}{3} + \dfrac{2}{3} × \dfrac{2}{2} = 4$

▪︎$\dfrac{3}{6}x - \dfrac{2}{6}x + \dfrac{15}{6} + \dfrac{4}{6} = 4$

▪︎$\dfrac{1}{6}x + \dfrac{19}{6} = 4$

☆ According to note second point ( Transposing )~

▪︎$\dfrac{1}{6}x = 4 - \dfrac{19}{6}$

☆ L.C.M = 6~

▪︎$\dfrac{1}{6}x = 4 × \dfrac{6}{6} - \dfrac{19}{6} × \dfrac{1}{1}$

▪︎$\dfrac{1}{6}x = \dfrac{24}{6} - \dfrac{19}{6}$

▪︎$\dfrac{1}{6}x = \dfrac{5}{6}$

▪︎$x = \dfrac{5}{6} ÷ \dfrac{1}{6}$

☆ Reciprocating the divided term~

▪︎$x = \dfrac{5}{6} × \dfrac{6}{1}$

▪︎$x = \dfrac{30}{6}$

☆ After dividing~

▪︎$x = 5$

$\huge\pink{The \ \ value \ \ of \ \ x = 5}$

Checking:-

♤ Let's check according to note third point~

• $\dfrac{1}{2} ( x + 5 ) - \dfrac{1}{3} ( x - 2 ) = 4 \implies ?$

♤ Applying the value of "x"~

• $\dfrac{1}{2} ( 5 + 5 ) - \dfrac{1}{3} ( 5 - 2 ) = 4 \implies ?$

• $\dfrac{1}{2} ( 10 ) - \dfrac{1}{3} ( 3 ) = 4 \implies ?$

• $\dfrac{1}{2} × 10 - \dfrac{1}{3} × 3 = 4 \implies ?$

• $\dfrac{10}{2} - \dfrac{3}{3} = 4 \implies ?$

♤ L.C.M = 6~

• $\dfrac{10}{2} × \dfrac{3}{3} - \dfrac{3}{3} × \dfrac{2}{2} = 4 \implies ?$

• $\dfrac{30}{6} - \dfrac{6}{6} = 4 \implies ?$

• $\dfrac{24}{6} = 4 \implies ?$

♤ After dividing 24 by 6~

• $4 = 4 \implies ✔$

$\huge\green{Hence, Proved : The \ \ value \ \ of \ \ x = 5}$

Answer:-

Hence, The value of x = 5.

:)