4 = 4
*
1 point
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property
Substitution Property
Reflexive Property
Symmetric Property
Transitive Property
The property being illustrated here is the Reflexive Property. It states that any number, when equated to itself, is always equal. In this case, the equation 4 = 4 demonstrates the reflexive property.
The step-by-step explanation for the equation "4 = 4" is as follows:
1. 4 is equal to 4.
- This is a given fact or starting point.
2. Multiplication Property of Equality: Multiply both sides by 1.
- When you multiply any number by 1, the value remains the same.
3. The equation becomes 4 * 1 = 4 * 1.
- Multiplying both sides of the equation by 1 does not change the value of either side.
4. Simplify both sides of the equation.
- Multiplying any number by 1 gives the same number.
5. The equation simplifies to 4 = 4.
- After simplification, both sides of the equation remain equal.
Therefore, the answer is 4 = 4, using the Multiplication Property of Equality.
The equation 4 = 4 represents a simple numerical equation where both sides of the equation are equal. In this case, the equation is already solved and does not require any manipulation to determine the value.
However, the properties you mentioned are general properties of equality that are used in algebraic equations to manipulate and simplify them. Let's briefly explain each property:
1. Addition Property of Equality: This property states that if you add the same number to both sides of an equation, the equality is still maintained. For example, if you have the equation x + 2 = 8, you can add 5 to both sides to get x + 2 + 5 = 8 + 5, which simplifies to x + 7 = 13.
2. Subtraction Property of Equality: This property is similar to the addition property, but it involves subtracting the same number from both sides of an equation. For instance, if you have the equation x - 3 = 10, you can subtract 2 from both sides to get x - 3 - 2 = 10 - 2, which simplifies to x - 5 = 8.
3. Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same number, the equality remains. For example, if you have the equation 2x = 12, you can multiply both sides by 3 to get 3 * 2x = 3 * 12, which simplifies to 6x = 36.
4. Division Property of Equality: This property is the inverse of the multiplication property and states that if you divide both sides of an equation by the same non-zero number, the equality is preserved. For instance, if you have the equation 8x = 40, you can divide both sides by 8 to get 8x / 8 = 40 / 8, which simplifies to x = 5.
5. Distributive Property: This property allows you to distribute a factor across the terms in parentheses. It is often used while simplifying expressions rather than solving equations. For example, in the expression 2(3 + x), you can use the distributive property to get 2 * 3 + 2 * x, which simplifies to 6 + 2x.
6. Substitution Property: This property allows you to replace a variable with its known value. It is commonly used when you solve one equation and substitute the value of the variable into another equation. For example, if you have the equations y = 3x and x = 4, you can substitute x = 4 into the first equation to get y = 3 * 4, which simplifies to y = 12.
7. Reflexive Property: This property states that any quantity is equal to itself. For example, for any value of x, you can write x = x.
8. Symmetric Property: This property states that if a = b, then b = a. For example, if you have the equation 2x = 8, you can say that 8 = 2x.
9. Transitive Property: This property states that if a = b and b = c, then a = c. For example, if you have the equations x = 4 and 4 = 2y, you can say that x = 2y.
These properties are important tools in algebraic manipulation and can be used effectively to solve equations or simplify expressions.