Inequalities, Expressions, and Equations

What is an inequality?

• treating two numbers the same

• the relation between two expressions that are not equal

• an inverse operation

Inequality symbols:

• show if one value is equal to another

• show if one value is less than, greater than, or not equal to another value

• are not valid unless two values are equal

What is a solution set?

• a set of values that do not satisfy a given set of equations or inequalities

• the solution to an inequality

• the set of values that satisfy a given set of equations or inequalities

What is the definition of one solution?

• no matter what constant is substituted in for the variable, the equation is ALWAYS true

• only this ONE solution will make the equation true

• no matter what constant is substituted in for the variable, the equation will NEVER be true

2x > 12

• x > 6

• x < 6

• x ≥ 6

• x ≤ 6

"Twenty-four minus three times an integer, x, is less than x minus four."

Write an inequality, in terms of x, to represent this information.

Mathematical Equivalence

OFF

2 + 3x ≤ 20

• x ≤ 6

• x ≥ -6

• x ≤ 7

• x ≥ -7

Match the following

• inequality

• equation

• expression

Combine like terms:

• similar solutions to different problems

• a process used to simplify an expression - terms that have the same variable part are combined using addition or subtraction

• multiplying the simplest form of an equation to find the distributive property of a solution

What is an equation?

• the steps to solving a mathematical problem

• a mathematical statement containing an equals sign,

  to show that two expressions are equal

• a fixed quantity that does not vary