Question

Below are the steps to solve an equation:

Step 1: |x - 4|+ 1 = 8
Step 2: |x - 4| = 8 - 1
Step 3: |X - 4| = 7
Which of the following is a correct next step to solve the equation?

Answer 1

After reaching the step |x - 4| = 7, the next step is to consider the definition of absolute value and set up two separate equations, x - 4 = 7 and x - 4 = -7, to solve for x. The solutions are x = 11 and x = -3, and it's important to check these solutions in the original equation for validity.

Step-by-step explanation:

To solve the equation |x - 4| + 1 = 8, where we have reached the step |x - 4| = 7, the next step involves addressing the absolute value. The property of absolute value states that if |a| = b, then a = b or a = -b, where b must be non-negative since absolute value cannot be negative. Applying this to our equation:

1. x - 4 = 7
2. x - 4 = -7

Now solve for x in each case:

1. x = 7 + 4
2. x = -7 + 4

Which simplifies to:

1. x = 11
2. x = -3

Therefore, we have two potential solutions to the equation, which are x = 11 and x = -3. It is important to check these solutions in the original equation to ensure that they make sense and are reasonable.