AnswersMathematics 8Solving with the Distributive Property — QuizQuestion 5
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Solving with the Distributive Property — Quiz

Question 5 • Mathematics 8

Henry showed all the steps he took to solve the equation. 4 times open paren negative 1 half x plus 7 close paren plus 5 x is equal to 15 Step Simplified Expression 1 negative 2 x plus 28 plus 5 x is equal to 15 2 3 x plus 28 is equal to 15 3 3 x is equal to 15 4 x is equal to 5 Sammy tried to verify the solution by substituting x is equal to 5 back into the original equation. It did not result in a true statement. Which explains why Henry’s solution is incorrect?

Answer
A
Step 1 is wrong because the distributive property of equality was used incorrectly.
B
Step 2 is wrong because the addition property of equality was used incorrectly.
C
Step 3 is wrong because the subtraction property of equality was used incorrectly.
D
Step 4 is wrong because the division property was used incorrectly.

Explanation

Steps 1 and 2 are correct: distributing gives −2x + 28 + 5x, which combines to 3x + 28 = 15. To isolate 3x, Henry needed to subtract 28 from both sides, giving 3x = 15 − 28 = −13. Step 3 incorrectly leaves the right side as 15, so the subtraction property was used incorrectly.

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