Question

How do you solve \[ - 2x > 6\]?

Answer 1

Hint: In this question we have asked to solve the linear inequality. Linear inequality can be defined as the inequality that holds a linear function. When two real numbers or algebraic expressions are expressed in symbols like $ < ,\, > $ or $ \leqslant ,\, \geqslant $, they can be called an inequality. For example- $2x < 10,\,\,3x < 9$. We solve these types of questions by taking all constant terms on one side and all terms containing $x$ to the other sides and after that we simplify the equation to get the required result.

Complete step by step answer:
Linear inequality can be defined as the inequality that holds a linear function or it can be defined as an inequality in one variable that can be written in the form $ax + b < 0$ where $a$ and $b$ are real numbers and $a \ne 0$. A linear function can be defined as a function whose graph is a straight line.

When two real numbers or algebraic expressions are expressed in symbols like $ < ,\, > $ or $ \leqslant ,\, \geqslant $, they can be called an inequality. When we solve an inequality it means to find a range, or ranges of values, that an unknown $x$ can take and satisfy the inequality. We have to solve the inequality \[ - 2x > 6\]. Dividing the whole equation by $ - 2$. We get,
$ \Rightarrow \dfrac{{ - 2x}}{{ - 2}} > \dfrac{6}{{ - 2}}$
On solving the above equation and changing the direction of inequality as we have divided it by a negative number. We get,
$ \Rightarrow x < - 3$

Therefore, the solution of the given inequality \[ - 2x > 6\] is$( - \infty , - 3)$.

Note: While solving the problems of inequalities first drag all the terms containing variables to one side and those with constant to the other side and then simplify the equation. Note that if the coefficient of the variable is positive then the direction of inequality will not change but if the coefficient is negative then the direction of the inequality changes.