Question

How do you find \[5x-7 < 2x-1\] ?

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 make the equation in a way that variables come one side so that we can get the solution by applying some properties of inequality on the equation.

Complete step-by-step answer:
Let us first understand the concept of inequalities before proceeding.
Inequalities that have the same solution are called equivalent. There are properties of inequalities as well as there were properties of equality. All the properties below are also true for inequalities involving \[\le \] and \[\ge \] .
The addition property of inequality says that adding the same number to each side of the inequality produces an equivalent inequality
If \[x > y\] , then \[x+z > y+z\]
If \[x < y\] , then \[x+z > y+z\]
The subtraction property of inequality tells us that subtracting the same number from both sides of an inequality gives an equivalent inequality.
If \[x > y\] , then \[x-z < y-z\]
If \[x < y\] , then \[x-z < y-z\]
Division of both sides of an inequality with a positive number produces an equivalent inequality.
If \[x > y\] and \[z > 0\] ,then \[\dfrac{x}{z} > \dfrac{y}{z}\]
If \[x < y\] and \[z > 0\] ,then \[\dfrac{x}{z} < \dfrac{y}{z}\]
Given equation is
 \[5x-7 < 2x-1\]
Now we will use the basic properties mentioned above description.
Subtracting \[2x\] on both sides of equation
 \[\Rightarrow 5x-7-2x < 2x-1-2x\]
 \[\Rightarrow 3x-7 < -1\]
Now add \[1\] on both sides of equation
 \[\Rightarrow 3x-7+1 < -1+1\]
 \[\Rightarrow 3x-6 < 0\]
Now add \[6\] on both sides of equation
 \[\Rightarrow 3x-6+6 < 6+0\]
 \[\Rightarrow 3x < 6\]
Now divide with 3 on both sides of equation
 \[x < 2\]
From this we can conclude that \[5x-7 < 2x-1\] = \[x < 2\]

Note: We can also do it in another way. We can do it by subtracting 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.