How do you know if a value is a solution for an inequality? how is this different from deyermining if a value is a solution to the equation?

To know whether a particular value is a
solution:

When both sides of an equation are algebraic
expresions we put the solution value of the variable in place of the variable in the
expressions. We arrive at a value in the left and another value in the right. Then the
equality does not hold. If the calculared values are equal on both side, then we say the
euality hods. Or equality is true.

In case of an inequality
like the expression on the left < epression on the right, we  put the solution
value for the unknown in left  and right side. The calculated value on the left should
be less than the calculated value on the right then the inequality
 holds.

Examples:

7x+1  = 
5x+11

We verify if x = 4 is a
solution.

Left side value with x =4.: 7*4+1 =
29.

Right side value with x =4 : 5*4 +11 =
31.

  29 is not equal to 31. So  x =4 is not a
solution.

Try with any other values for
x.

5 x < 3x+for inequality:
10.

5x-3x < 10.

2x
< 10

Divide by 2:

x
<  5

This means for any  x < 5 is a solution.
1 is a solution.. Because if we put x =1, in 5x < 3x+10, we
get:

 5*1 <
3*1+10.  

  5 <
13.

Similarly , we can verify if 6 is a
solution:

5*6 < 
3*5+10

30 < 15 +10

30
< 25. How this this. This is because we tried whether 6 is solution. So it is not
a solution.