Question

The table shows the solution to the equation |2x − 5| − 2 = 3:

Step 1 |2x − 5| = 3 + 2
Step 2 |2x − 5| = 5
Step 3 2x − 5 = 5 or 2x − 5 = −5
Step 4 2x = 10 or 2x = 0
Step 5 x = 5 or x = 0
Which is the first incorrect step? (1 point)

a
Step 3

b
Step 4

c
Step 5

d
Solution is correct

Answer 1

Given : \[|2x − 5| − 2 = 3\]

Step-by-step : First off, start by adding 2 to both sides\[|2x−5|−2+2=3+2\]\[|2x−5|=5\]Solve for absolute value \[|2x−5|=5\]In that case, we know it may be\[ 2x−5=5\]or\[2x−5=−5\]So let's go over our possibilities.

Possibility #1 : \[2x−5=5\]
Add 5 to both sides\[2x−5+5=5+5\]\[2x=10\]Now divide both sides by 2\[\frac{ 2x }{ 2 }=\frac{ 10 }{ 2 }\]\[x=5\]

Possibility #2 : \[2x−5=−5\]
Add 5 to both sides\[2x−5+5=−5+5\]\[2x=0\]Divide both sides by 2\[\frac{ 2x }{ 2 }=\frac{ 0 }{ 2 }\]\[x=0\]

Now from both possibilities, it's either \[x=5\]or\[x=0\]