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How do you find 5x7<2x1 ?

Answer
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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 and .
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 xz<yz
If x<y , then xz<yz
Division of both sides of an inequality with a positive number produces an equivalent inequality.
If x>y and z>0 ,then xz>yz
If x<y and z>0 ,then xz<yz
Given equation is
 5x7<2x1
Now we will use the basic properties mentioned above description.
Subtracting 2x on both sides of equation
 5x72x<2x12x
 3x7<1
Now add 1 on both sides of equation
 3x7+1<1+1
 3x6<0
Now add 6 on both sides of equation
 3x6+6<6+0
 3x<6
Now divide with 3 on both sides of equation
 x<2
From this we can conclude that 5x7<2x1 = 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.

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