Daniela's error occurred in trying to simplify the equation [tex]\(13x + 42 = 276\)[/tex]. Let's identify the correct steps she should have taken:
1. Start with the given equation:
[tex]\[
13x + 42 = 276
\][/tex]
2. To isolate the term with [tex]\(x\)[/tex], we need to eliminate the constant term on the left side by subtracting 42 from both sides:
[tex]\[
13x + 42 - 42 = 276 - 42
\][/tex]
3. Simplifying both sides results in:
[tex]\[
13x = 234
\][/tex]
4. Next, to solve for [tex]\(x\)[/tex], we need to divide both sides of the equation by 13:
[tex]\[
x = \frac{234}{13}
\][/tex]
5. Performing the division gives us:
[tex]\[
x = 18.0
\][/tex]
Daniela's mistake was in the second step, where instead of subtracting 42, an error was introduced in the calculation. The correct property she needed to use to avoid this mistake is the subtraction property of equality. This property states that subtracting the same amount from both sides of an equation keeps the equation balanced.
Thus, the correct answer is:
subtraction property of equality.
