# What are the 5 steps to solving inequalities?

## What are the 5 steps to solving inequalities?

To solve an inequality, we can:

1. Add the same number to both sides.
2. Subtract the same number from both sides.
3. Multiply both sides by the same positive number.
4. Divide both sides by the same positive number.
5. Multiply both sides by the same negative number and reverse the sign.

## What are the 4 properties of inequality?

Properties of inequality

• Addition property: If x < y, then x + z < y + z.
• Subtraction property: If x < y, then x − z < y − z.
• Multiplication property:
• z > 0. If x < y, and z > 0 then x × z < y × z.
• z < 0. If x < y, and z < 0 then x × z > y × z.
• Division property:
• It works exactly the same way as multiplication.
• z > 0.

What is the golden rule for solving inequalities?

The Golden Rule of Inequalities Whenever you MULTIPLY or DIVIDE both sides of an inequality by a NEGATIVE NUMBER, you must flip the inequality symbol.

### What is the formula of inequality?

a) 2x < 5. Here, when we divide both sides by 2, which is a positive number, the sign of inequality does not change. So the correct inequality is x < 5/2….Solved Examples on Inequalities.

Interval Random Number Checking the Inequality
(2, 5) 3 32 – 7(3) + 10 < 0 -2 < 0, true
(5, ∞) 6 62 – 7(6) + 10 < 0 4 < 0, false

### What are the 6 properties of equality?

The Reflexive Property. a =a.

• The Symmetric Property. If a=b, then b=a.
• The Transitive Property. If a=b and b=c, then a=c.
• The Substitution Property. If a=b, then a can be substituted for b in any equation.
• The Addition and Subtraction Properties.
• The Multiplication Properties.
• The Division Properties.
• The Square Roots Property*
• What is an inequality solution?

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.

## What is the first rule of solving an equation?

Parentheses are the first operation to solve in an equation. If there are no parentheses, then move through the order of operations (PEMDAS) until you find an operation you do have and start there.

## What is Bodmas rule in maths?

BODMAS rule is an acronym to help children to remember the order of operations in calculations. Operations are simply the different things that we can do to numbers in maths. It stands for, ‘Brackets, Order, Division, Multiplication, Addition, Subtraction. This is also the same for addition and subtraction.

What are the rules for solving an inequality?

If a < b,then a+c < b+c.

• If a < b,then a – c < b – c.
• If a < b and if c is a positive number,then a · c < b · c.
• If a < b and if c is a positive number,then.
• If a < b and if c is a negative number,then a · c > b · c.
• If a < b and if c is a negative number,then.
• ### What are the steps to solving equations and inequalities?

– Combine like terms on the right side of the inequality: 3 x + 2 < 6 + 2 x {\\displaystyle 3x+2<6+2x} – Move the variable to one side by subtracting 2 x {\\displaystyle 2x} from both sides: 3 x + 2 − 2 x < 6 + 2 x − 2 x – Isolate the variable by subtracting 2 from both sides: x + 2 − 2 < 6 − 2 {\\displaystyle x+2-2<6-2} x < 4 {\\displaystyle x<4}

### How do you solve one step inequalities?

– Represent inequalities on a number line. – Use the addition property of inequality to isolate variables and solve algebraic inequalities, and express their solutions graphically. – Use the multiplication property of inequality to isolate variables and solve algebraic inequalities, and express their solutions graphically.

What is the difference between solving equations and inequalities?

The main difference between inequalities and equations is in terms of their definitions that clearly delineate their functionalities in mathematical operations.

• The second seminal difference between the two is in terms of what they each represent.
• The symbols used to express equality and inequality in each of these are also different.