Question
This is Daniela’s work to solve the equation 13 x + 42 = 276.
13 x + 42 = 276. 13 x = 318. x = 24 and StartFraction 6 Over 13 EndFraction.
Which property did Daniela need to use to avoid her error?
division property of equality
multiplication property of equality
subtraction property of equality
identity property of equality
13 x + 42 = 276. 13 x = 318. x = 24 and StartFraction 6 Over 13 EndFraction.
Which property did Daniela need to use to avoid her error?
division property of equality
multiplication property of equality
subtraction property of equality
identity property of equality
Answers
GPT-4o mini
To identify the property that Daniela needed to use to avoid her error, we first analyze her work.
Daniela starts with the equation:
\[ 13x + 42 = 276 \]
She incorrectly finds that:
\[ 13x = 318 \]
The correct step, using the **subtraction property of equality**, would have been to subtract 42 from both sides:
\[ 13x + 42 - 42 = 276 - 42 \]
This simplifies to:
\[ 13x = 234 \]
The next step, dividing both sides by 13, would then give:
\[ x = 18 \]
Since Daniela made a mistake by arriving at 318 instead of 234, she needed to apply the **subtraction property of equality** correctly to avoid her error.
Therefore, the correct answer is:
**subtraction property of equality**.
Daniela starts with the equation:
\[ 13x + 42 = 276 \]
She incorrectly finds that:
\[ 13x = 318 \]
The correct step, using the **subtraction property of equality**, would have been to subtract 42 from both sides:
\[ 13x + 42 - 42 = 276 - 42 \]
This simplifies to:
\[ 13x = 234 \]
The next step, dividing both sides by 13, would then give:
\[ x = 18 \]
Since Daniela made a mistake by arriving at 318 instead of 234, she needed to apply the **subtraction property of equality** correctly to avoid her error.
Therefore, the correct answer is:
**subtraction property of equality**.