To determine which property justifies step 1 in solving the equation:
[tex]$
8x + 15 = 11x + 2
$[/tex]
Step 1 given is:
[tex]$
8x = 11x - 13
$[/tex]
Let’s analyze how we go from the initial equation to this step.
The initial equation is:
[tex]$
8x + 15 = 11x + 2
$[/tex]
We subtract [tex]\(2\)[/tex] from both sides:
[tex]$
8x + 15 - 2 = 11x
$[/tex]
This simplifies to:
[tex]$
8x + 13 = 11x
$[/tex]
Then, we subtract [tex]\(8x\)[/tex] from both sides:
[tex]$
13 = 3x
$[/tex]
This can be rewritten as:
[tex]$
8x = 11x - 13
$[/tex]
So, we have used subtraction to isolate terms involving [tex]\(x\)[/tex]. Specifically, we subtracted [tex]\(8x\)[/tex] from both sides of the equation:
[tex]$
8x + 15 - 8x = 11x + 2 - 8x
$[/tex]
The subtraction of [tex]\(8x\)[/tex] from both sides leads us to:
[tex]$
15 = 3x + 2
$[/tex]
Which can then be rewritten to focus on isolating [tex]\(x\)[/tex]:
[tex]$
8x = 11x - 13
$[/tex]
Thus, the property of equality used to justify step 1 is:
B. the subtraction property of equality
