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 and put an inequality sign in its place, is there ever a time when the same value will be a solution to both the equation and inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.

Question

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 and put an inequality sign in its place, is there ever a time when the same value will be a solution to both the equation and inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.

I am still getting confused with this.

Answer 1

I can;t really explain it but here is an example x+5<10. look at the x we know the value of it must be a number that when added to 5 will not make it be more than 10, because the inequality sign represents(less than). so first you must see what the inequality symbol represesnts. x+5<10 we know the value oc x has to be less than 5.

Answer 2

To determine if a value is a solution for an inequality, you can substitute the value into the inequality and check if the resulting statement is true. If it is true, then the value is a solution to the inequality. If it is false, then the value is not a solution.

This process is different from determining if a value is a solution to an equation. In an equation, you need to find the value(s) that make both sides of the equation equal. In contrast, an inequality asks if a value makes the inequality statement true or false.

In some cases, there can be values that are solutions to both an equation and an inequality when you replace the equal sign with an inequality sign. For example, if you have the equation 2x + 3 = 9 and the inequality 2x + 3 > 9, you can see that when x = 3, it is a solution to both. However, this is not always the case as the solutions to the inequality may be different from the solutions to the equation.

Let's take the inequality 4x - 5 > 7 as an example. Now, we can check if a value, such as x = 4, is a solution or not.

Substituting x = 4 into the inequality:

4(4) - 5 > 7
16 - 5 > 7
11 > 7

Since the resulting statement 11 > 7 is true, we can conclude that x = 4 is a solution to the inequality 4x - 5 > 7.

Hope this helps clarify the differences and the process of determining solutions to inequalities!