Formula
Which property of equality is shown: a = a
Reflexive Property of Equality
Is a symbolic expression of the fact that two things are equal.
Equality
A mathematical statement that compares two values or expressions that are not equal, using symbols like <, >, ≤, ≥, or ≠.
Inequality
Solve for y: 3y = 18
y = 6
Which property of equality is shown: a = b, then b = a
Symmetric Property of Equality
This property states that if a = b, then b = a.
Symmetric Property of Equality
If both sides of an inequality are multiplied by the same positive number, the inequality remains the same.
Multiplication Property of Inequality
Solve for x: 2x - 5 = 11
Step 1: 2x = 16
Step 2: x = 16 ÷ 2 = 8
If a < b, then a + c < b + c. What property is being shown?
Addition Property of Inequality
If one quantity equals a second, and the second quantity equals a third, then the first quantity equals the third.
Transitive Property of Equality
If a < b and b < c, then a < c. What property of Inequality is this?
Transitive Property of Inequality
Solve for z: 5z + 12 = 2z + 21
z = 3
If a < b and c > 0, then a⁄c < b/c. What property is this?
Division Property of Inequality
If x=y, then y can be substituted for x in any expression containing x in the equation.
Substitution Property of Equality
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.
Solve the inequality for x: −3x + 7 ≤ 1
x ≥ 2
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
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.
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
Solve the inequality for y: 4y−7 > 5y+2
y < −9