Question

1 Q3: Consider solving the equation: 2(4x + 1) - 3 = ax + b Which statements are true about the solution to the equation when substituting values a and bas specified? Select all that apply. 1. If a = 8 and b = 1, then there is no solution. 2. If a = 4 and b = -2, then there is no solution. 3. If a = 8 and b = -1, then there is exactly one solution. 4. If a = 2 and b = -1, then there is exactly one solution. 5. If a = 2 and b = 4, then there are infinitely many solutions. =

Answer 1

`2(4x+1)-3=ax+b`

To find the solution of this equation you solve for x, you leave the terms with x in one side of the equation:

a. Remove the parenthesis: multiply 2 by the two terms in the parenthesis:

`8x+2-3=ax+b`

b. Leave in one side all the terms with x:

`\begin{gathered} 8x-ax=b-2+3 \\ 8x-ax=b+1 \end{gathered}`

Then, for the given statements:

1. If a =8 and b= 1
`\begin{gathered} 8x-8x=1+1 \\ 0=0 \end{gathered}`

Then, the whit those values for a and b the equation has as solution all the real numbers, because 0=0.

Statement: False

2. If a = 4 and b = -2
`\begin{gathered} 8x-4x=-2+1 \\ 4x=-1 \\ x=-(1)/(4) \end{gathered}`

Then, the whit those values for a and b the equation has exactly one solution x= -1/4

Statement: False

3. If a = 8 and b = -1
`\begin{gathered} 8x-8x=-1+1 \\ 0=0 \end{gathered}`

Then, the whit those values for a and b the equation has as solution all the real numbers, because 0=0.

Statement: False

4. If a = 2 and b = -1
`\begin{gathered} 8x-2x=-1+1 \\ 6x=0 \\ x=(0)/(6) \\ x=0 \end{gathered}`

Then, the whit those values for a and b the equation has exactly one solution x=0

Statement: True

5. If a = 2 and b = 4
`\begin{gathered} 8x-2x=4+1 \\ 6x=5 \\ x=(5)/(6) \end{gathered}`

Then, the whit those values for a and b the equation has exactly one solution x=5/6

Statement: False