Question

1. complete the tables to determine if the expressions are equivalent. if the expressions are equivalent, name the property or properties that make them equivalent.

3(a - 5)

a	value of expression
2
3

3a - 15

a	value of expression
2
3

Explanation:

To solve this, we'll calculate the value of each expression for \( a = 1, 2, 3 \) and \( x = 1, 2, 3 \) (assuming the tables are for these values, though the image is a bit unclear, we'll proceed with the given expressions \( 3(a - 5) \) and \( 3x - 15 \), noting they are equivalent by the distributive property \( 3(a - 5)=3a - 15 \)).

For \( 3(a - 5) \) (let's use \( a \) values 1, 2, 3):

Step 1: When \( a = 1 \)

Substitute \( a = 1 \) into \( 3(a - 5) \):
\( 3(1 - 5)=3(-4)= -12 \)

Step 2: When \( a = 2 \)

Substitute \( a = 2 \):
\( 3(2 - 5)=3(-3)= -9 \)

Step 3: When \( a = 3 \)

Substitute \( a = 3 \):
\( 3(3 - 5)=3(-2)= -6 \)

For \( 3x - 15 \) (let's use \( x \) values 1, 2, 3):

Step 1: When \( x = 1 \)

Substitute \( x = 1 \):
\( 3(1) - 15 = 3 - 15 = -12 \)

Step 2: When \( x = 2 \)

Substitute \( x = 2 \):
\( 3(2) - 15 = 6 - 15 = -9 \)

Step 3: When \( x = 3 \)

Substitute \( x = 3 \):
\( 3(3) - 15 = 9 - 15 = -6 \)

Table for \( 3(a - 5) \) (with \( a = 1, 2, 3 \)):

\( a \)	Value of \( 3(a - 5) \)
2	-9
3	-6

Table for \( 3x - 15 \) (with \( x = 1, 2, 3 \)):

\( x \)	Value of \( 3x - 15 \)
2	-9
3	-6

Since the values match for corresponding inputs, the expressions \( 3(a - 5) \) and \( 3x - 15 \) are equivalent (by the distributive property: \( 3(a - 5)=3a - 15 \), and here \( x \) is a variable, so replacing \( a \) with \( x \) shows the same equivalence).

Final Answer (for the tables, values as calculated):

For \( 3(a - 5) \): \( -12, -9, -6 \) (for \( a = 1, 2, 3 \))
For \( 3x - 15 \): \( -12, -9, -6 \) (for \( x = 1, 2, 3 \))
The expressions are equivalent by the distributive property.

Answer:

To solve this, we'll calculate the value of each expression for \( a = 1, 2, 3 \) and \( x = 1, 2, 3 \) (assuming the tables are for these values, though the image is a bit unclear, we'll proceed with the given expressions \( 3(a - 5) \) and \( 3x - 15 \), noting they are equivalent by the distributive property \( 3(a - 5)=3a - 15 \)).

For \( 3(a - 5) \) (let's use \( a \) values 1, 2, 3):

Step 1: When \( a = 1 \)

Substitute \( a = 1 \) into \( 3(a - 5) \):
\( 3(1 - 5)=3(-4)= -12 \)

Step 2: When \( a = 2 \)

Substitute \( a = 2 \):
\( 3(2 - 5)=3(-3)= -9 \)

Step 3: When \( a = 3 \)

Substitute \( a = 3 \):
\( 3(3 - 5)=3(-2)= -6 \)

For \( 3x - 15 \) (let's use \( x \) values 1, 2, 3):

Step 1: When \( x = 1 \)

Substitute \( x = 1 \):
\( 3(1) - 15 = 3 - 15 = -12 \)

Step 2: When \( x = 2 \)

Substitute \( x = 2 \):
\( 3(2) - 15 = 6 - 15 = -9 \)

Step 3: When \( x = 3 \)

Substitute \( x = 3 \):
\( 3(3) - 15 = 9 - 15 = -6 \)

Table for \( 3(a - 5) \) (with \( a = 1, 2, 3 \)):

\( a \)	Value of \( 3(a - 5) \)
2	-9
3	-6

Table for \( 3x - 15 \) (with \( x = 1, 2, 3 \)):

\( x \)	Value of \( 3x - 15 \)
2	-9
3	-6

Since the values match for corresponding inputs, the expressions \( 3(a - 5) \) and \( 3x - 15 \) are equivalent (by the distributive property: \( 3(a - 5)=3a - 15 \), and here \( x \) is a variable, so replacing \( a \) with \( x \) shows the same equivalence).

Final Answer (for the tables, values as calculated):

For \( 3(a - 5) \): \( -12, -9, -6 \) (for \( a = 1, 2, 3 \))
For \( 3x - 15 \): \( -12, -9, -6 \) (for \( x = 1, 2, 3 \))
The expressions are equivalent by the distributive property.