Question

How do you find \[3\left( 2-3x \right)>4\left( 1-4x \right)\]?

Answer 1

Hint: We can solve the inequality equations just like we solve normal equations. It is the basic concept in solving a single linear equation. To solve this problem we must know the basic identities of Inequalities. When we start solving the equation first we have to remove parentheses on both sides of the equation. After that we have to make the equation in a way that all the terms containing variables come one side so that we can get the solution by applying some properties of inequality on the equation.

Complete step by step solution:
Given equation is
\[3\left( 2-3x \right)>4\left( 1-4x \right)\]
First we have to remove the parentheses by multiplying LHS with 3 and the RHS with 4.
After multiplying we will get
\[\Rightarrow 6-9x>4-16x\]
Now we will use the basic properties mentioned above.
 Now we had to add 16x on both sides of equation
\[\Rightarrow 6-9x+16x>4-16x+16x\]
By simplifying we will get
\[\Rightarrow 6+7x>4\]
Now we will subtract 6 from both sides of the equation.
\[\Rightarrow 7x+6-6>4-6\]
By simplifying we will get
\[\Rightarrow 7x>-2\]
Now divide with 7 on both sides of the equation.
By dividing we will get
\[\Rightarrow \dfrac{7x}{7}>\dfrac{-2}{7}\]
Simplifying above equation will give
\[\Rightarrow x>-\dfrac{2}{7}\]
From this we can conclude that from the given equation we get \[x>-\dfrac{2}{7}\]
In decimal form we can write this as
\[\Rightarrow x>-0.2857\].

Note: We can also do it in another way. After removing parentheses we can subtract the whole right side equation from the left side equation and by performing certain operations as we did in the above method also gives the solution. We can solve this question in many ways but we must have to know basic properties of inequalities.