Question

Find the solution of the following equation $5\left( 3x+5 \right)=2\left( 7x-4 \right)$.
(a) 17
(b) 33
(c) -33
(d) -17

Answer 1

Hint:We will first simplify both sides of the equation and then we will transpose both equations in LHS and then solve this equation accordingly using some basic mathematical operation.

Complete step-by-step answer:
It is given in the question to find the solution of the equation $5\left( 3x+5 \right)=2\left( 7x-4 \right)$. We know that if we have two integers, then we can multiply them using some rules as shown below:
\[\left( + \right)\times \left( + \right)=+\]
\[~\left( - \right)\times \left( - \right)=+\]
\[\left( - \right)\times \left( + \right)=-\]
\[\left( + \right)\times \left( - \right)=-\]
We will first expand both the sides by using distributive property i.e $a(b+c)=ab+ac$
Now apply the property in above equation in both L.H.S and R.H.S,
We can see that 5 and 3x are positive, so using the rule, we will get +15x. Similarly, 5 and 5 are positive integers, so we will get +25.
Similarly for RHS We can see that 2 and 7x are positive, so using the rule, we will get +14x. And, 2 is positive and -4 is negative integer, so we will get -8.
Therefore, we get the following modified equation $15x+25=14x-8$. Now we will transfer or transpose $14x$ to LHS from RHS and transpose 25 from LHS to RHS. Therefore equation becomes $15x-14x=-8-25$ simplifying further we get $x=-33$.
Thus the value of x in the given equation is -33, and option c) is the correct answer.

Note: This is a very basic question of the polynomial but usually students make mistakes in transposing and taking sign with terms,So it is recommended to do calculation carefully.And For adding of two negative numbers,we have to just add the absolute value of each number together (without considering the sign) and then put a negative sign in front of resulting answer.