Question

The equation 7(u−5)=−21 is solved in several steps below. For each step, choose the reason that best justifies it.

7(u−5)=−21
(A) Given equation

7u−35=−21
(B) _________________

7u−35+35=−21+35
(C) _________________

7u=14
(D) _________________

u=2
(E) _________________

Answer 1

The equation 7(u-5)=-21 is solved using the Distributive Property, Addition Property of Equality, Simplification, and Division Property of Equality. Each step systematically isolates the variable and simplifies the equation, leading to the solution u=2.

Step-by-step explanation:

The equation 7(u−5)=−21 is solved in several steps below. For each step, choose the reason that best justifies it.

• 7(u−5)=−21 (A) Given equation
• 7u−35=−21 (B) Distributive Property: This step involves multiplying the 7 by both terms inside the parentheses, (u) and (−5).
• 7u−35+35=−21+35 (C) Addition Property of Equality: This step involves adding 35 to both sides of the equation to isolate the variable term 7u.
• 7u=14 (D) Simplification: After adding 35 to both sides, the equation simplifies to 7u equals 14.
• u=2 (E) Division Property of Equality: Divide both sides by 7 to solve for u.

Throughout the solution, we eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.