Question

solve the problem...LINEAR EQUATIONS IN ONE VARIABLE (7a-6 ) / 3 = ( 3a+1 ) /2

Answer 1

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Answer 2

Answer:

• Value of a is 3.

Step-by-step explanation:

$\bf{Q)}\;\sf{\dfrac{7a-6}{3}=\dfrac{3a+1}{2}}$

To Find:

• Value of a.

Solution:

$\sf{\implies\dfrac{7a-6}{3}=\dfrac{3a+1}{2}}$

By cross-multiplication,

$\sf{\implies2(7a-6)=3(3a+1)}$

Opening the brackets,

$\sf{\implies14a-12=9a+3}$

Transposing variables to LHS, constants to RHS and changing their sign,

$\sf{\implies14a-9a=3+12}$

Solving further,

$\sf{\implies5a=15}$

Transposing 5 from LHS to RHS and changing its sign,

$\sf{\implies a=\dfrac{15}{5}}$

Dividing the numbers,

$\implies \underline{\boxed{\bf{a=3}}}$

Hence,

• a = 3

Verification:

To verify we will substitute the value of a to the LHS and RHS, and see if they are equal or not.

LHS:

$\sf{\longmapsto\dfrac{(7\times3)-6}{3}}$

$\sf{\longmapsto\dfrac{21-6}{3}}$

$\sf{\longmapsto\dfrac{15}{3}}$

$\sf{\longmapsto5}$

RHS:

$\sf{\longmapsto\dfrac{(3\times3)+1}{2}}$

$\sf{\longmapsto\dfrac{9+1}{2}}$

$\sf{\longmapsto\dfrac{10}{2}}$

$\sf{\longmapsto5}$

As,

• LHS = RHS

Hence, verified.