Question

Solve \[5x + \dfrac{7}{2} = \dfrac{3}{2}x - 14\].

Answer 1

Hint:Here, we are given only one variable in the equation. So, we need to find the value of x when we are given this equation. Any term of an equation may be taken from one side to other with the change in its sign, this does not affect the equality of the statement and this process is called transposition. The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS).

Complete step by step answer:
Given equation is as below,
\[5x + \dfrac{7}{2} = \dfrac{3}{2}x - 14\]
By transposing the above equation, we get,
\[ \Rightarrow 5x = \dfrac{3}{2}x - 14 - \dfrac{7}{2}\]
Again by transposing the above equation, we get,
\[ \Rightarrow 5x - \dfrac{3}{2}x = - 14 - \dfrac{7}{2}\]
Taking LCM as 2 on both the sides, we get,
\[ \Rightarrow \dfrac{{5x(2) - 3x}}{2} = \dfrac{{ - 14(2) - 7}}{2}\]
Simplify the above equation, we get,
\[ \Rightarrow \dfrac{{10x - 3x}}{2} = \dfrac{{ - 28 - 7}}{2}\]
\[ \Rightarrow \dfrac{{7x}}{2} = \dfrac{{ - 35}}{2}\]
Dividing by 2 on both the side, we get,
\[ \Rightarrow 7x = - 35\]
\[ \Rightarrow x = \dfrac{{ - 35}}{7}\]
\[ \therefore x = - 5\]

Thus, the value for the equation \[5x + \dfrac{7}{2} = \dfrac{3}{2}x - 14\] is\[x = - 5\].
Let's see if the answer is correct or not. First we will calculate the LHS part.
So, \[LHS =5x + \dfrac{7}{2}\]
Substituting the value of x, we get,
\[LHS = 5( - 5) + \dfrac{7}{2}\]
Simplify the above expression, we get,
\[ LHS= - 25 + \dfrac{7}{2}\]
Taking LCM as 2, we get,
\[ LHS= \dfrac{{ - 25(2) + 7}}{2}\]
\[\Rightarrow LHS= \dfrac{{ - 50 + 7}}{2}\]
Simplify the above expression, we get,
\[\therefore LHS= \dfrac{{ - 43}}{2}\]

Next, we will calculate the RHS part.
\[RHS = \dfrac{3}{2}x - 14\]
Substituting the value of x, we get,
\[RHS = \dfrac{3}{2}( - 5) - 14\]
\[\Rightarrow RHS = \dfrac{{ - 15}}{2} - 14\]
Taking LCM as 2, we get,
\[RHS = \dfrac{{ - 15 - 14(2)}}{2}\]
Simplify the above expression, we get,
\[ RHS= \dfrac{{ - 15 - 28}}{2}\]
\[\therefore RHS = \dfrac{{ - 43}}{2}\]

Thus, LHS = RHS and so the answer is correct. Hence, it is verified.

Note:An algebraic equation is an equality involving variables i.e. equality sign (=). An algebraic equation is an equality involving variables, where the values of the expressions on the LHS and RHS are equal. We can verify the answer by putting the value of $t$ in the above equation and check if LHS = RHS, then the answer is correct.