Answer :
[tex]2(4x+1)-3=ax+b[/tex]
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:
[tex]8x+2-3=ax+b[/tex]b. Leave in one side all the terms with x:
[tex]\begin{gathered} 8x-ax=b-2+3 \\ 8x-ax=b+1 \end{gathered}[/tex]Then, for the given statements:
1. If a =8 and b= 1 [tex]\begin{gathered} 8x-8x=1+1 \\ 0=0 \end{gathered}[/tex]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[tex]\begin{gathered} 8x-4x=-2+1 \\ 4x=-1 \\ x=-\frac{1}{4} \end{gathered}[/tex]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[tex]\begin{gathered} 8x-8x=-1+1 \\ 0=0 \end{gathered}[/tex]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[tex]\begin{gathered} 8x-2x=-1+1 \\ 6x=0 \\ x=\frac{0}{6} \\ x=0 \end{gathered}[/tex]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[tex]\begin{gathered} 8x-2x=4+1 \\ 6x=5 \\ x=\frac{5}{6} \end{gathered}[/tex]Then, the whit those values for a and b the equation has exactly one solution x=5/6
Statement: False
