Question

Choose all the equations that have a= -1/2 as a solution.A.) 2a/7 - 6/7 = 5/7B.) 4a/7 + 3/7 = 1/7C.) 2a/7 + 6/7 = 5/7D.) 4a/7 - 3/7 = 1/7

Answer 1

B and C

Step-by-step explanation:

To be able to determine all of the equations that have a = -1/2 as a solution, we'll substitute a = -1/2 into all of the equations and see which ones give us the value at the right-hand side of the equation.

A.

`\begin{gathered} (2)/(7)(-(1)/(2))-(6)/(7)=(5)/(7) \\ -(1)/(7)-(6)/(7)=(5)/(7) \\ (-1-6)/(7)=(5)/(7) \\ -(7)/(7)\\e(5)/(7) \\ -1\\e(5)/(7) \end{gathered}`

Since both sides of the equation are not equal, then a = -1/2 is not a solution of the equation.

B.

`\begin{gathered} (4)/(7)(-(1)/(2))+(3)/(7)=(1)/(7) \\ -(2)/(7)+(3)/(7)=(1)/(7) \\ (-2+3)/(7)=(1)/(7) \\ (1)/(7)=(1)/(7) \end{gathered}`

Since both sides of the equation are equal, then a = -1/2 is a solution to the equation.

C.

`\begin{gathered} (2)/(7)(-(1)/(2))+(6)/(7)=(5)/(7) \\ -(1)/(7)+(6)/(7)=(5)/(7) \\ (-1+6)/(7)=(5)/(7) \\ (5)/(7)=(5)/(7) \end{gathered}`

Since both sides of the equation are equal, then a = -1/2 is a solution to the equation.

D.

`\begin{gathered} (4)/(7)(-(1)/(2))-(3)/(7)=(1)/(7) \\ -(2)/(7)-(3)/(7)=(1)/(7) \\ (-2-3)/(7)=(1)/(7) \\ -(5)/(7)\\e(1)/(7) \end{gathered}`

Since both sides of the equation are not equal, then a = -1/2 is not a solution of the equation.