AnswersMathematics 8Solving with the Distributive Property — QuizQuestion 1
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Solving with the Distributive Property — Quiz

Question 1 • Mathematics 8

Sarita showed the steps to solving the equation. 5 times open paren x minus 3 close paren plus 7 times open paren x plus 4 close paren is equal to 73 Steps Sarita’s Solution Sarita’s Verification 1 5 x minus 15 plus 7 x plus 28 is equal to 73 5 times open paren 5 minus 3 close paren plus 7 times open paren 5 plus 4 close paren is equal to 73 5 times negative 2 plus 7 times 9 is equal to 73 negative 10 plus 63 is equal to 73 53 is not equal to 73 2 open paren 5 plus 7 close paren times x plus open paren negative 15 plus 28 close paren is equal to 73 3 12 x plus 13 is equal to 73 4 12 x is equal to 60 5 x is equal to 5 When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?

Answer
A
Sarita was supposed to add the 5 and 7 in the first step.
B
Sarita was supposed to use the division property of equality in the third step.
C
Sarita’s solution is correct. She made an error in her verification.
D
Sarita added plus 13 instead of negative 13 in the fourth step.

Explanation

Sarita’s algebra is correct: distributing gives 5x − 15 + 7x + 28 = 73, which simplifies to 12x + 13 = 73. Subtracting 13 gives 12x = 60, so x = 5. To verify, 5 − 3 = 2, so the left side is 5(2) + 7(9) = 10 + 63 = 73. Her verification incorrectly treated 5 − 3 as −2; the solution is correct, but the verification has an error.

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