Question

How do you solve \[ - 8x - 10 = 4x + 14\]?

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘x’ terms one side and constants on the other side of the equation.

Complete step-by-step solution:
Given, \[ - 8x - 10 = 4x + 14\].
We transpose ‘4x’ which is present in the right hand side of the equation to the left hand side of the equation by subtracting ‘4x’ on the left hand side of the equation.
\[\Rightarrow - 8x - 4x - 10 = 14\]
\[\Rightarrow - 12x - 10 = 14\]
We transpose negative 10 to the right hand side of the equation by adding 10 on the right hand side of the equation.
\[ \Rightarrow - 12x = 14 + 10\].
\[\Rightarrow - 12x = 24\]
Divide by -12 on both sides of the equations we have,
\[\Rightarrow x = - \dfrac{{24}}{{12}}\]
\[\Rightarrow x = - 2\]. This is the required answer.

Note: Since we have a polynomial of degree two and hence it is called quadratic polynomial. If we have a polynomial of degree ‘n’ then we have ‘n’ roots. In the given problem we have a degree that is equal to 2. Hence the number of roots are 2. We use a quadratic formula if we are unable to split the middle term that fails to factorize. Quadratic formula and Sridhar’s formula are both the same. We know that the product of two negative numbers gives us a positive number. Also keep in mind when shifting values from one side of the equation to another side of the equation, always change sign from positive to negative and vice-versa.