Below are the steps to solve an equation:
Step 1: |x − 2| + 3 = 7
Step 2: |x − 2| = 7 − 3
Step 3: |x − 2| = 4
Which of the following is a correct next step to solve the equation?
x + 2 = −4
−x − 2 = 4
x + 2 = 4
x − 2 = −4
is it d
yes, it is, though I would have written it
-(x-2) = 4 (why might that be?)
Extra credit. What is a different correct step (not shown)?
You gotta put the 7 in the spot were in fits bruh
Below are the steps to solve an equation:
Step 1: |x − 2| + 3 = 7
Step 2: |x − 2| = 7 − 3
Step 3: |x − 2| = 4
Which of the following is a correct next step to solve the equation?
Yes, the correct next step to solve the equation |x − 2| = 4 is x - 2 = -4 (option d).
To explain why, let's go through the steps again:
Step 1: |x − 2| + 3 = 7
Step 2: |x − 2| = 7 − 3
Step 3: |x − 2| = 4
In step 2, we subtracted 3 from both sides of the equation to isolate the absolute value expression on the left side.
Now, to eliminate the absolute value, we need to consider two cases:
Case 1: (x - 2) ≥ 0
If (x - 2) is positive or zero, then |x - 2| = x - 2. So, we can rewrite the equation as (x - 2) = 4.
Case 2: (x - 2) < 0
If (x - 2) is negative, then |x - 2| = -(x - 2), because the absolute value of a negative number is its positive counterpart. Rewriting the equation, we get -(x - 2) = 4.
Now, let's solve for x in both cases:
Case 1: (x - 2) = 4
Simplifying this equation, we get x = 6.
Case 2: -(x - 2) = 4
Multiplying through by -1, we get -x + 2 = 4.
Simplifying this equation, we get -x = 2, and by multiplying both sides by -1, we get x = -2.
So, we have two possible solutions: x = 6 and x = -2.
Therefore, the correct next step to solve the equation |x − 2| = 4 is x - 2 = -4 (option d).