Equations and Fair Pay Vocabulary Review Sheet

How to Use

• Review each term and definition before your quiz.
• Study how math, real-life, and fairness examples connect to the idea of equal pay for equal work.
• Keep this sheet in your Equity in Numbers Student Journal to review before assessments.
• Remember: Equations show balance — and fairness means keeping both sides equal in life and math.

Equation

• Definition: A mathematical sentence showing that two expressions are equal, using an equals sign (=).
• Math Examples:
  • (x + 3 = 18)
  • (2x + 4 = 10)
  • (x – 5 = 12)
• Real-Life Example: Finding out how much someone earns when you know their pay difference.
• Fairness Example: Equations help us calculate how much to adjust pay so that everyone earns fairly for the same work.

Variable

• Definition: A symbol (usually a letter) that stands for an unknown number.
• Math Examples:
  • (x) = Worker B’s hourly wage.
  • In (x + 3 = 18), (x) is what we are solving for.
• Real-Life Example: A company might not know the fair wage yet—so we use a variable until we solve for it.
• Fairness Example: Variables represent the unknowns in real-world justice—what needs to change for things to be equal.

Solve

• Definition: To find the value of a variable that makes the equation true.
• Math Examples:
  • (x + 3 = 18 → x = 18 – 3 → x = 15)
  • (x – 2 = 10 → x = 12)
• Real-Life Example: Figuring out what pay rate balances the equation between two workers.
• Fairness Example: Solving shows how much change is needed to reach fairness in pay.

Balance

• Definition: Keeping both sides of an equation equal by doing the same operation on each side.
• Math Examples:
  • Add or subtract the same number on both sides:
    (x + 3 = 18 → x = 15).
• Real-Life Example: Making sure pay increases or decreases are applied fairly.
• Fairness Example: A balanced equation is like fair treatment — both sides get the same value.

Wage Gap

• Definition: The difference in pay between two people doing the same or similar work.
• Math Examples:
  • Worker A = $18/hr; Worker B = $15/hr → Gap = $3/hr.
  • Represented as (x + 3 = 18).
• Real-Life Example: Comparing pay between teachers and engineers, or men and women in similar jobs.
• Fairness Example: Solving wage-gap equations helps expose and correct unfair pay differences.

Unknown

• Definition: The number we don’t know yet in an equation—often represented by a variable.
• Math Examples:
  • In (x + 5 = 30), the unknown is (x = 25).
  • In (x + 4 = 22), the unknown is (x = 18).
• Real-Life Example: Finding how much someone should earn to make pay equal.
• Fairness Example: The unknown represents the fairness we’re solving for — what’s missing to create equality.

Substitution

• Definition: Replacing a variable with its value to check that both sides of the equation are equal.
• Math Examples:
  • (x = 15); check: (15 + 3 = 18 → 18 = 18). ✅
• Real-Life Example: Testing if the raise truly closes the wage gap.
• Fairness Example: Substitution confirms whether balance—and fairness—has been achieved.

Equality

• Definition: The state of two things being the same in value, expression, or treatment.
• Math Examples:
  • (18 = 18) or (x + 3 = 18) when solved correctly.
• Real-Life Example: Equal pay for equal work.
• Fairness Example: Equality in math models equality in life — everyone deserves the same value for the same contribution.

Inequality

• Definition: A math statement showing that two values are not equal, using symbols like >, <, ≥, ≤.
• Math Examples:
  • (15 < 18) or (x + 3 < 18).
• Real-Life Example: When one worker earns less than another for the same job.
• Fairness Example: Inequalities reveal gaps we must close to achieve true fairness.

Fair Pay

• Definition: When people are paid equally for doing the same work with the same skill and effort.
• Math Examples:
  • Worker A: $18/hr, Worker B: $15/hr → Needs +$3 raise for fairness.
• Real-Life Example: Adjusting salaries to make them equal across job sectors.
• Fairness Example: Fair pay supports dignity, justice, and equity in every profession.

✅ Summary of Math + Fairness Connections

Concept	Math Focus	Fairness Connection
Equation	Keeps both sides equal	Models fairness and balance
Variable & Unknown	Represents missing value	Shows what must change to make things fair
Wage Gap	Measures pay difference	Highlights inequality that can be fixed
Balance & Equality	Equal operations both sides	Reflects justice and equal treatment
Fair Pay	Solving for fairness	Ensures all workers are valued equally