Question

Choose all that correctly identify the algebraic property that justifies the step.

Answer 1

Subtraction property of equality:

$8x-8x-6=9x-8x-24$

Distributive property:

$3x-6+5x=9x-24$

Commutative property of addition:

$3x+5x-6=9x-24$

Addition property of equality:

$-6x+24=x-24+24$

Why?

We are asked to identify the algebraic property that justifies the step, so let's check every equation and their next second steps to identify the algebraic property that match with them.

First:

$8x-6=9x-24$

Here, we can check that in the second step, the subtraction property of equality is applied. The factor "8X" was subtracted to both sides of the equations resulting in the following equation:

$8x-8x-6=9x-8x-24\\\\-6=x-24\\\\x=18$

Second:

$3(x-2)+5x=9x-24$

Here, we can check that in the second step, the distributive property is applied, the expression inside the parenthesis is multiplied by an external number (3), resulting in the following equation:

$3x-6+5x=9x-24$

Third:

$3x-6+5x=9x-24$

Here, we can check that in the second step, the commutative property of addition is applied, the like terms were grouped to make the operations easier to perform, resulting in the following equation:

$3x+5x-6=9x-24$

Fourth:

$-6=x-24$

Here, we can check that in the second step, the addition property of equality is applied. The factor "24" was added to both sides of the equations resulting in the following equation:

$-6+24=x-24+24$

Have a nice day!

Answer 2

Answer:

Answer Key

8x − 6 = 9x − 24

8x − 8x − 6 = 9x − 8x − 24

Subtraction Property of Equality

3(x − 2) + 5x = 9x − 24

3x − 6 + 5x = 9x − 24

Distributive Property

3x − 6 + 5x = 9x − 24

3x + 5x − 6 = 9x − 24

Commutative Property of Addition

−6 = x − 24

−6 + 24 = x − 24 + 24

Addition Property of Equality

Step-by-step explanation: Select all of them.