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Formula
Equalities
Inequalities
Solving
100

Which property of equality is shown: a = a

Reflexive Property of Equality

100

Is a symbolic expression of the fact that two things are equal.

Equality

100

A mathematical statement that compares two values or expressions that are not equal, using symbols like <, >, ≤, ≥, or ≠.

Inequality

100

Solve for y: 3y = 18

y = 6

200

Which property of equality is shown: a = b, then b = a

Symmetric Property of Equality

200

This property states that if a = b, then b = a.

Symmetric Property of Equality

200

If both sides of an inequality are multiplied by the same positive number, the inequality remains the same.

Multiplication Property of Inequality

200

Solve for x: 2x - 5 = 11

Step 1: 2x = 16

Step 2: x = 16 ÷ 2 = 8

300

If a < b, then a + c < b + c. What property is being shown?

Addition Property of Inequality

300

If one quantity equals a second, and the second quantity equals a third, then the first quantity equals the third.

Transitive Property of Equality

300

If a < b and b < c, then a < c. What property of Inequality is this?

Transitive Property of Inequality

300

Solve for z: 5z + 12 = 2z + 21

z = 3

400

If a < b and c > 0, then a⁄c  < b/c. What property is this?

Division Property of Inequality

400

If x=y, then y can be substituted for x in any expression containing x in the equation.

Substitution Property of Equality

400

When will the sense of inequality change? (Can only be applied in the multiplication property of inequality)

When multiplying or dividing both sides of the inequality by a negative real number.

400

Solve the inequality for x: −3x + 7 ≤ 1

x ≥ 2

500

A teacher says: “If you have the same number of stickers as your classmate, and your classmate has the same number as another, then you both have the same number.” Which property of equality is she demonstrating?

Transitive Property of Equality

500

Which of the following statements is true based on the properties of equality?

A. If 𝑥 > 3, then 2𝑥 > 6 must always be true.

B. If 𝑥 < 5, then 𝑥 - 2 > 3 must be true.

C. If 𝑥 = 7, then 𝑥 - 4 > 4 must be true.

D. If 𝑥 > 2, then -𝑥 > -2 must be true.

A. If 𝑥 > 3, then 2𝑥 > 6 must always be true.

500

Which of the following inequalities is equivalent to |𝑥 - 3| < 5?

A. 𝑥 - 3 > 5 or 𝑥 - 3 < -5

B. 𝑥 - 3 < 5 and 𝑥 - 3 > -5

C. 𝑥 > 8 or 𝑥 < -2

D. 𝑥 < 8 and 𝑥 > -2

D. 𝑥 < 8 and 𝑥 > -2

500

Solve the inequality for y: 4y−7 > 5y+2

y < −9