To determine which property Sanjay used to show that [tex]\(7x + 42 = 42\)[/tex] is equivalent to [tex]\(7x = 0\)[/tex], let's carefully look at the steps he followed:
1. The equation begins with [tex]\(7(x + 6) = 42\)[/tex].
2. Expanding the left side using the distributive property gives [tex]\(7x + 42 = 42\)[/tex].
3. Sanjay then isolates the term involving [tex]\(x\)[/tex] by eliminating the constant on the left side. He does this by subtracting 42 from both sides of the equation:
[tex]\[
7x + 42 - 42 = 42 - 42
\][/tex]
4. Simplifying this, we get:
[tex]\[
7x = 0
\][/tex]
The property used in step 3, where Sanjay subtracts 42 from both sides to isolate [tex]\(7x\)[/tex], is called:
Subtraction property of equality.
Hence, Sanjay used the subtraction property of equality to determine that [tex]\(7x + 42 = 42\)[/tex] is equivalent to [tex]\(7x = 0\)[/tex].
