a. 10x-6=44b. (x+3)-15=48c. 4(x+6)-10=26d. 3(x+3)-15=48e.Which two equations have the same solution set? Write a sentence explaining how the properties of equality can be used to determine the pair without having to find the solution set for each.
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a.
[tex]\begin{gathered} 10x-6=44 \\ 10x=44+6 \\ 10x=50 \\ x=\frac{50}{10} \\ x=5 \end{gathered}[/tex]b.
[tex]\begin{gathered} 9(x+3)-15=48 \\ 9x+27-15=48 \\ 9x+12=48 \\ 9x=36 \\ x=\frac{36}{9} \\ x=4 \end{gathered}[/tex]c.
[tex]\begin{gathered} 4(x+6)-10=26 \\ 4x+24-10=26 \\ 4x+14=26 \\ 4x=26-14 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]d.
[tex]\begin{gathered} 3(x+3)-15=48 \\ 3x+9-15=48 \\ 3x-6=48 \\ 3x=48+6 \\ 3x=54 \\ x=\frac{54}{3} \\ x=18 \end{gathered}[/tex]The answer in set notation
[tex]x=\mleft\lbrace5,4,3,18\mright\rbrace[/tex]e. Equation b and Equation d have the same solution set . Both of the equations is equals to 48.