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.

Answer 1

The only difference in solving an inequality and an equation is when you multiply or divide both sides by negative numbers. Then it reverses the direction of the carat.

> = more than
< = less than

Your last sentence does not make sense to me. Are there typos?

Answer 2

To determine if a value is a solution for an inequality, you need to substitute the value into the inequality and check if it satisfies the inequality.

For example, let's consider the inequality 2x + 3 > 7. To check whether a value, say x = 2, is a solution to this inequality, you would substitute x = 2 into the inequality:

2(2) + 3 > 7
4 + 3 > 7
7 > 7

In this case, 2 is not a solution because 7 is not greater than 7.

Determining if a value is a solution to an equation is different because in an equation, you are trying to find the specific value(s) that make both sides of the equation equal. To determine if a value is a solution to an equation, you substitute the value into the equation and check if it holds true.

For example, consider the equation 2x + 3 = 7. To check whether x = 2 is a solution, you substitute x = 2 into the equation:

2(2) + 3 = 7
4 + 3 = 7
7 = 7

In this case, 2 is a solution because both sides of the equation are equal.

When replacing the equal sign in an equation with an inequality sign, there can be instances where the same value is a solution to both the equation and inequality. For example, let's take the equation above and turn it into an inequality:

2x + 3 ≥ 7

In this case, if we substitute x = 2 into the inequality:

2(2) + 3 ≥ 7
4 + 3 ≥ 7
7 ≥ 7

Here, 2 is a solution to both the equation and inequality because both sides of the equation and the inequality are equal in this instance.

To provide an example of an inequality where a value may or may not be a solution, consider the inequality:

5x - 2 < 13

In this case, we can try substituting x = 3 into the inequality:

5(3) - 2 < 13
15 - 2 < 13
13 < 13

Here, 3 is not a solution because 13 is not less than 13.