Question

Solve the following equations for x and name the property used for each:

1. (8 = 8 + x)
2. (10x = 10)
3. (5 × 1/5 = x)
4. (2 + 8 = 8 + x)

Answer 1

To solve the set of equations for x, we apply properties such as the Subtraction Property of Equality, Division Property of Equality, and the Multiplicative Inverse. In all cases, algebraic manipulation results in finding the value of x.

Step-by-step explanation:

Step-by-Step Explanation of Solutions to Equations

For the given set of equations, we solve for x and mention the relevant property used in each solution:

1. (8 = 8 + x) - To find x, we need to get x by itself on one side of the equation. Subtracting 8 from both sides gives us 0 = x. The property used here is the Subtraction Property of Equality, which states that if you subtract the same number from both sides of an equation, the two sides remain equal.
2. (10x = 10) - To solve for x, we divide both sides of the equation by 10, giving us x = 1. The property used here is the Division Property of Equality, which states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal.
3. (5 × 1/5 = x) - Multiplying 5 by 1/5 gives us 1, so x = 1. This uses the property of Multiplicative Inverse, where any number multiplied by its reciprocal equals 1.
4. (2 + 8 = 8 + x) - This equation can be simplified to 10 = 8 + x. Subtracting 8 from both sides, we find that x = 2. The property used here is the Subtraction Property of Equality.