11
practice testMultiple Choice

Practice Test

Question 11 • Mathematics 8

To solve the equation, Antwan uses the distributive property, combines like terms, then uses the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible values of the constant after Antwan has completed these steps? 3 times open paren 1 third x plus 1 close paren plus 4 is equal to negative 1 minus 4 times open paren x plus 3 close paren

Answer
A
negative 3 or 3
B
negative 3 or 5
C
negative 20 or 5
D
negative 20 or 20

Explanation

Distribute and combine like terms: 3(⅓x + 1) + 4 = x + 7, and −1 − 4(x + 3) = −4x − 13. This gives x + 7 = −4x − 13, so moving the variable terms together and the constants to the other side gives 5x = −20. If the terms are moved in the opposite direction, the equivalent equation is −5x = 20; therefore, the possible constants are −20 or 20.

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