Answer:
Explanation:
1.Do 4x and 15 + x have the same value when x is 5?
To determine if 4x and 15 + x have the same value when x is 5, we can substitute 5 for x in both expressions and see if they equal the same value:
4x = 4 * 5 = 20
15 + x = 15 + 5 = 20
So, when x is 5, 4x and 15 + x both have the same value of 20.
2. Are 4x and 15 + x equivalent expressions?
Two expressions are considered equivalent if they have the same value for all possible values of the variables they contain. In this case, for all values of x, 4x and 15 + x will have the same value, so we can say that 4x and 15 + x are equivalent expressions.
Also:
When we substitute x = 5 into both expressions 4x and 15 + x, we find that:
4x = 4 * 5 = 20
15 + x = 15 + 5 = 20
As we can see, both expressions have the same value of 20 when x = 5. This means that the value of the expression 4x is equal to the value of the expression 15 + x when x = 5.
However, just because the values of the expressions are equal when x = 5, this does not necessarily mean that the expressions are equivalent for all values of x. To determine if two expressions are equivalent, we need to consider their values for all possible values of the variables they contain. In this case, since 4x and 15 + x have the same value for all values of x, we can conclude that these two expressions are equivalent.
In general, equivalent expressions are expressions that have the same value for all values of the variables they contain. Equivalent expressions can be transformed into each other through operations such as adding or subtracting the same value, multiplying or dividing by the same non-zero value, or using the distributive property.