How do you know if a value is a solution for an inequality?How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.

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How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.

say

x<12
to check if something is a solution, try it. Like say the number 5
5 < 12 yes, it works

the solution to the equality and inequality can only be the same if the inequality includes the equality. For example:
x</= 12 means x less than or equal to 12
In that case 12 witself would be a solution to both equality and inequality.
However 12 is not less than 12 so it would not be a solution to
x<12

To determine if a value is a solution for an inequality, you need to substitute the value into the inequality and check if the inequality holds true. If the inequality is satisfied, then the value is a solution; otherwise, it is not.

This process is different from determining if a value is a solution to an equation. For an equation, you substitute the value into the equation and check if both sides are equal. If they are, then the value is a solution; otherwise, it is not.

In some cases, replacing the equal sign of an equation with an inequality sign can yield the same value as a solution for both the equation and the inequality. For example, consider the equation 2x = 8. The value x = 4 is a solution to this equation. If we replace the equal sign with an inequality sign, such as 2x ≤ 8, the value x = 4 is still a solution to this inequality. This happens when the inequality is "less than or equal to" or "greater than or equal to," as these include the equality case as a valid solution.

Now, let's write an inequality and provide a value that may or may not be a solution:

Inequality: 3x + 5 > 10

For example, let's check if x = 2 is a solution:

Substituting x = 2 into the inequality, we have:
3(2) + 5 > 10
6 + 5 > 10
11 > 10

Since 11 is greater than 10, the inequality holds true when x = 2. Hence, x = 2 is a solution to the inequality 3x + 5 > 10.