Question

How do you solve and check your solution to \[ - \dfrac{2}{7}v = 16\]?

Answer 1

Hint:Here in this we have to solve the given equation and it is in the form of an algebraic equation. Solving this equation, we have to find the unknown value v. The LHS of the given equation is in the form of fraction. by using the simple multiplication and division we find the value of x.

Complete step by step explanation:
The given equation is an algebraic equation. The algebraic equation is a combination of variable and constant which has an equal sign. Here the equation is in the form of fraction in LHS. So we use multiplication and division or arithmetic operations and solve for further
Now consider the given equation
\[ - \dfrac{2}{7}v = 16\]
Multiply by 7 on the both sides of the equation we get
\[ \Rightarrow - \dfrac{2}{7}v \times 7 = 16 \times 7\]
On multiplying we get
\[ \Rightarrow - 2v = 112\]
Now divide the above equation by -2 we get
\[ \Rightarrow v = \dfrac{{ - 112}}{2}\]
First we simplify the above fraction
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 56 and 112
The factors of 2 are 1 and 2
Therefore the common factor for the both 112 and 2 is 2. So we divide the both numbers by 2 we get
\[ \Rightarrow v = - 56\]
Therefore, the value of v is -56
Since the dividend is a negative quantity then the negative sign is carried out by the quotient.
We can also verify the given question by substituting the value of v.
Consider \[ - \dfrac{2}{7}v = 16\]. Substitute the value of x as -8.5 so we have
\[ \Rightarrow - \dfrac{2}{7}\left( { - 56} \right) = 16\]
On simplification we get
\[ \Rightarrow 16 = 16\]
Hence LHS is equal to RHS.

Note: If the algebraic expression contains only one unknown, we determine the value by using simple multiplication and division. The function contains a fraction then there is no change in solving the algebraic expression. The tables of multiplication should be known to solve these kinds of problems.