Question

How do you solve $ 6\left( {3x - 4} \right) > - 6 $ ?

Answer 1

Hint: This question is related to linear inequalities. A relation which holds between two values when they are different is known as inequality. Any two real numbers or algebraic expressions when related by ‘ $ < $ ’, ‘ $ > $ ’, ‘ $ \leqslant $ ’ or ‘ $ \geqslant $ ’ form a linear inequality. The notation referred to in the given question is ‘ $ > $ ’ which means that the algebraic expression $ 6\left( {3x - 4} \right) $ is greater than $ - 6 $ . There are various types of inequalities: numerical inequalities, variable inequalities, double inequalities, strict inequalities, slack inequalities, linear inequalities in one variable, linear inequalities in two variables and quadratic inequalities. The given question is a type of inequalities with multiplication and division.

Complete step-by-step solution:
Given inequality is $ 6\left( {3x - 4} \right) > - 6 $ .
In order to solve this question, first, we distribute $ 6\left( {3x - 4} \right) $ and we get,
 $
   \Rightarrow 6\left( {3x - 4} \right) > - 6 \\
   \Rightarrow 18x - 24 > - 6 \\
  $
Add $ 24 $ on both the sides of inequality which will isolate the $ x $ term while keeping inequality balanced.
 $
   \Rightarrow 18x - 24 + 24 > - 6 + 24 \\
   \Rightarrow 18x > 18 \\
  $
Now, we divide both sides of inequality by $ 18 $ . This will help us to solve for the value of $ x $ while keeping the inequality balanced at the same time.
 $
   \Rightarrow \dfrac{{18x}}{{18}} > \dfrac{{18}}{{18}} \\
   \Rightarrow x > 1 \\
  $
Hence, the answer is $ x > 1 $ .

Note: While solving the question, the students should ensure that the inequality symbol should not change by mistake. There are certain rules of inequality which need to be followed while solving inequality problems. Some of them are:
-Only equal numbers should be added or subtracted from both the sides of inequality.
-Both the sides of inequality can only be multiplied and divided with the same positive number.