Question

Match the labels to the steps in solving the equation 6x - 9 = 45.

Step Statements Reasons
1 6x - 9 = 45 Given
2 6x - 9 + 9 = 45 + 9 Addition property of equality
3 6x = 54 Simplification
4 x = 9 Division property of equality

Answer 1

To solve the equation 6x - 9 = 45, one must apply the given, addition property of equality, simplification, and division property of equality in sequence and then check that the solution is reasonable.

Step-by-step explanation:

Steps in Solving the Equation 6x - 9 = 45

To solve the equation 6x - 9 = 45, we follow a series of algebraic steps. Here is how you match the labels to the steps:

1. Given: The problem presents you with the initial equation 6x - 9 = 45.
2. Addition property of equality: Add 9 to both sides of the equation to get 6x - 9 + 9 = 45 + 9. This step eliminates the -9 on the left-hand side, leaving you with just 6x.
3. Simplification: After adding, simplify the equation to get 6x = 54. You have removed the negative term and can now see what 6x equals.
4. Division property of equality: Divide both sides of the equation by 6 to isolate x, resulting in x = 54/6, which simplifies to x = 9.

Once you have found the value of x, you should always check your answer to ensure that it is reasonable and satisfies the original equation. Substituting x = 9 back into the initial equation should yield a true statement.