What are the rules for solving inequalities?

What are the rules for solving inequalities?

When solving an inequality: • you can add the same quantity to each side • you can subtract the same quantity from each side • you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.

What are the steps to solving linear inequalities?

1. Step 1: Solve the inequality for y.
2. Step 2: Graph the boundary line for the inequality.
3. Step 3: Shade the region that satisfies the inequality.
4. Step 4: Solve the second inequality for y.
5. Step 5: Graph the boundary line for the second inequality.
6. Step 6: Shade the region that satisfies the second inequality.

What’s the only rule for solving linear inequalities?

All but one of the rules for solving linear inequalities are the same as solving linear equations. If you divide or multiply an inequality by a negative number, reverse the inequality to obtain an equivalent inequality.

What are 3 ways to solve inequalities?

Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number. Swapping left and right hand sides.

How many solutions are there in a linear inequality?

Therefore, the solution set of a single linear inequality is always a half plane, so there are infinitely many solutions. So, for a linear inequality in two variables, there are infinitely many numbers of solutions.

How do you know if its a linear inequality?

A linear inequality contains one of the symbols of inequality:. It shows the data which is not equal in graph form. A linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign.

What are the properties of linear inequalities?

Linear Inequalities

• Transitive Property. If a < b and b < c then a < c.
• Addition Property. If a < b then a + c < b + c. Adding the same quantity to both sides of an inequality produces an equivalent inequality.
• Subtraction Property. If a < b then a – c < b – c.

What are basic property of addition of inequalities?

The addition property for inequalities states that if an inequality exists, adding or subtracting the same number on both sides does not change the inequality.

How to solve linear inequalities?

Solving linear inequalities of one variable involves various arithmetic operations such as addition, subtraction, multiplication and division. Also, the solution of the given inequality can be represented on the number line. Solving Linear Inequalities of Two Variables

When is an inequation said to be linear?

An inequation is said to be linear if the exponent of each variable occurring in it is first degree only, and there is no term involving the product of the variables.

How do you solve a linear equation with one variable?

Method to Solve a Linear Inequation in One Variable 1 Remove the fractions (or decimals) by multiplying both sides by an appropriate factor. 2 Put all variable terms on one side and all constants on the other side. 3 Make the coefficient of the variable 1. 4 Choose the solution set from the replacement set.

What is the difference between linear inequalities and multi step equations?

Linear Inequalities. Most of the rules or techniques involved in solving multi-step equations should easily translate to solving inequalities. The only big difference is how the inequality symbol switches direction when a negative number is multiplied or divided to both sides.