Name the property:
3x+5x
(3+5)x
transitive property of congruence
symmetric property of congruence
reflexive property of equality
symmetric property of equality
addition property of equality
division property of equality
substitution property
transitive property of equality
multiplication property of equality
distributive property
reflexive property of congruence
subtraction property of equality
(I honestly have no idea)
the "x" is DISTRIBUTED over the binomial
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The property you are referring to is the distributive property.
To understand how to identify properties in mathematical expressions, it is helpful to understand what each property represents.
1. Reflexive Property of Equality: This property states that any value or mathematical expression is always equal to itself. For example, a = a is an example of the reflexive property of equality.
2. Symmetric Property of Equality: This property states that if two values or mathematical expressions are equal, then they can be reversed in order. For example, if a = b, then b = a.
3. Transitive Property of Equality: This property states that if two values or mathematical expressions are equal to a third value or mathematical expression, then they are also equal to each other. For example, if a = b and b = c, then a = c.
4. Addition Property of Equality: This property allows you to add the same value or mathematical expression to both sides of an equation without changing its equality. For example, if a = b, then a + c = b + c.
5. Subtraction Property of Equality: This property allows you to subtract the same value or mathematical expression from both sides of an equation without changing its equality. For example, if a = b, then a - c = b - c.
6. Multiplication Property of Equality: This property allows you to multiply both sides of an equation by the same value or mathematical expression without changing its equality. For example, if a = b, then a * c = b * c.
7. Division Property of Equality: This property allows you to divide both sides of an equation by the same value or mathematical expression without changing its equality. For example, if a = b, then a / c = b / c.
8. Reflexive Property of Congruence: This property states that any shape or geometric figure is always congruent to itself. For example, triangle ABC is congruent to triangle ABC.
9. Symmetric Property of Congruence: This property states that if two shapes or geometric figures are congruent to each other, then they can be reversed in order. For example, if triangle ABC is congruent to triangle DEF, then triangle DEF is congruent to triangle ABC.
10. Transitive Property of Congruence: This property states that if two shapes or geometric figures are congruent to a third shape or geometric figure, then they are also congruent to each other. For example, if triangle ABC is congruent to triangle DEF and triangle DEF is congruent to triangle XYZ, then triangle ABC is congruent to triangle XYZ.
11. Substitution Property: This property allows you to replace a variable or expression with an equivalent value or expression. For example, if a = b, then you can substitute b for a in any equation or expression.
Now, going back to your initial question, 3x + 5x can be simplified by combining like terms. Since both terms have the variable x, you can add their coefficients to get 8x. So, 3x + 5x = 8x.
On the other hand, (3 + 5)x can also be simplified using the distributive property. The expression inside the parentheses can be simplified first as 3 + 5 = 8. Then, you can distribute the coefficient 8 to the variable x to get 8x. So, (3 + 5)x = 8x.
In summary, the property used to simplify both expressions is the distributive property.