Table of Contents

## Which is the solution to the inequality?

A “solution” of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.

## Is the given value a solution of the inequality?

A solution of an inequality is a value that makes the inequality true. An inequality can have more than one solution. The set of all solutions of an inequality is called the solution set. The symbol ≥/ means “is not greater than or equal to.”

**What is the solution to the equation?**

A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation. To find the solution to an equation means to find the value of the variable that makes the equation true.

**Which graph is the solution to the inequality?**

The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system. Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality.

### How do you know if a solution is an inequality?

Note: To see if an ordered pair is a solution to an inequality, plug it into the inequality and simplify. If you get a true statement, then the ordered pair is a solution to the inequality. If you get a false statement, then the ordered pair is not a solution.

### Which equation has no solution?

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.

**Can an equation have more than one solution?**

There can be more than one solution to a system of equations. A system of linear equations will have one point of intersection, or one solution. To graph a system of equations that are written in standard form, you must rewrite the equations in slope -intercept form.

**How are two inequalities with the same solution set solved?**

Two inequalities with the same solution set are equivalent inequalities. Inequalities are solved with the following properties of inequality. (The same number may be added to both sides of an inequality without changing the solution set.) (Both sides of an inequality may be multiplied by the same positive number without changing the solution set.)

#### How to solve inequality in the inequality calculator?

To solve your inequality using the Inequality Calculator, type in your inequality like x+7>9. The inequality solver will then show you the steps to help you learn how to solve it on your own. Type <= for “less than or equal to”. Here is an example: Type >= for “greater than or equal to”.

#### Is the original inequality satisfied by any number less than 4?

The original inequality is satisfied by any real number less than 4. The solution set can be written {x|x < 4}. A graph of the solution set is shown in Figure 2.6, where the parenthesis is used to show that 4 itself does not belong to the solution set.

**How to solve all inequalities with interval notation?**

From now on, the solutions of all inequalities will be written with interval notation. THREE-PART INEQUALITIES The inequality -2 < 5 + 3m < 20 in the next example says that 5 + 3m is between -2 and 20. This inequality can be solved using an extension of the properties of inequality given above, working with all three expressions at the same time.