Question

4x−1=−2(x+1) (Addition or Subtraction Property of equality

4x−1=−2x−2 (Addition OR Subtraction Property of Equality)
6x−1=−2 (Distributive Property)
6x=−1 ( Given)
x=−16 (Commutative property)
Put them in the right order.

Answer 1

The correct order to solve the equation 4x−1=2(x+1) involves four steps: applying the distributive property, the addition property of equality, the subtraction property of equality, and finally the division property of equality, resulting in the solution x=0.

Step-by-step explanation:

The given steps in the question appear to be mixed up and need to be put in the correct order to solve the equation 4x−1=2(x+1). The correct sequence is as follows:

1. Applying the Distributive Property: 4x−1=2(x+1) becomes 4x−1=−2x−2.
2. Using the Addition Property of Equality to move variables to one side: adding 2x to both sides gives 6x−1=−2.
3. Applying the Subtraction Property of Equality by adding 1 to both sides to isolate the variable term: 6x=−1+1, which simplifies to 6x=0.
4. Finally, using the Division Property of Equality to solve for x: dividing both sides by 6 results in x=0.

The solution is that x equals zero and not −16 as incorrectly listed. When it comes to exponents, it's important to remember the rules of signs and how negative exponents operate, such as x⁻⁴ = 1/x⁴, drawing on information that when a base is raised to a negative exponent, the result is the reciprocal of that base raised to the positive exponent.