Can linear inequalities have only one solution?

Can linear inequalities have only one solution?

Linear inequalities can either have no solution, one specific solution, or an infinite amount of solutions. Thus, the total possible would equal three. For instance, say we have a variable x. Although we do not know what x is, we can determine it’s value depending on what inequalities it has been placed next to.

What are the rules of linear inequalities?

Rules for Solving Inequalities

• Add the same number on both sides.
• From both sides, subtract the same number.
• By the same positive number, multiply both sides.
• By the same positive number, divide both sides.
• Multiply the same negative number on both sides and reverse the sign.

Do you think that there can be more than one solution to a linear inequality in one variable?

Inequalities typically have infinitely many solutions. The solutions are presented graphically on a number line or using interval notation or both. All but one of the rules for solving linear inequalities are the same as solving linear equations.

What does satisfy the inequality mean?

To show that substituting one or more variables into an equation or inequality “works out”. That is, the equation or inequality simplifies to a true statement. See also.

What is the solution set of the inequality?

The solution set of an inequality is the set of all solutions. Typically an inequality has infinitely many solutions and the solution set is easily described using interval notation. The solution set of example 1 is the set of all x <= 7.

What do solutions to inequalities look like?

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.

Can a system of linear inequalities have as its solution set all the points on the coordinate plane?

Linear inequalities can be graphed on a coordinate plane. The solutions for a linear inequality are in a region of the coordinate plane. A boundary line, which is the related linear equation, serves as the boundary for the region.

When can you say that a system of a linear inequalities has a solution no solution?

You can verify whether a point is a solution to a system of linear inequalities in the same way you verify whether a point is a solution to a system of equations. Systems of inequalities can have no solutions when boundary lines are parallel.