Question

The steps for solving an equation are shown below. Identify which property was used for each step.

2(5x - 7) = 2x + 10
10x - 14 = 2x + 10
-2x - 2x
8x - 14 = 10
+14 + 14
8x = 24
8/8
x = 3

A. Addition Property of Equality

B. Subtraction Property of Equality

C. Division Property of Equality

D. Distributive Property

Answer 1

The properties used in solving the algebraic equation include the Distributive Property, Subtraction Property of Equality, Addition Property of Equality, and Division Property of Equality. These steps simplify the equation to isolate the variable and determine its value.

Step-by-step explanation:

The steps for solving the equation 2(5x - 7) = 2x + 10 involve several properties of equality and arithmetic operations as follows:

1. Distributive Property: The equation begins with distributing the 2 across the terms within the parentheses resulting in 10x - 14 = 2x + 10.
2. Subtraction Property of Equality: To isolate the variable term on one side, the equation is subtracted by 2x from both sides to yield 8x - 14 = 10.
3. Addition Property of Equality: Adding 14 to both sides of the equation to eliminate the constant term on the left side gives 8x = 24.
4. Division Property of Equality: Finally, to solve for x, both sides of the equation are divided by 8, resulting in x = 3.

Each step simplifies the equation further until the variable is isolated and its value is determined. It is always important to eliminate terms wherever possible to simplify the algebra and then check the answer to see if it is reasonable.