Equations and Inequalities

Equations and inequalities are both mathematical sentences formed by relating two

expressions to each other. In an equation the two expressions are deemed equal which is shown by the symbol =.

x=y x is equal to y

Where as in an inequality the two expressions are not necessarily equal which is shown by the symbols: >, <, ≤ or ≥.

x>yx is greater than yx≥yx is greater than or equal to yx<yx is less than yx≤yx is less than or equal to y

An equation or an inequality that contains at least one variable is called an open sentence.

When you substitute the variable in an open sentence with a number the resulting statement is either true or false. If the statement is true the number is a solution to the equation or inequality.

Example

Is 3 a solution to

5x+14=24

Substitute x for 3

5⋅3+14

15+14=29≠24

FALSE!

Since 29 is not equal to 24, 3 is not a solution to the equation.

Example

Is 4 a solution to

4a−5<3+3a

Substitute a for 4

4⋅4−5<3+3⋅4

16−5<3+12

11<15

TRUE!

4 is a solution to the inequality.

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